Suppose ΔDEF has an exterior angle at vertex D. The measure of the exterior angle is (8x−2)º, m∠E=(3x−8)°, and m∠F=(4x+13)°. What is the measure of the exterior angle at vertex D?
A. 7°
B. 13°
C. 41°
D. 54°

Answers

Answer 1

The measure of the exterior angle at vertex D is: D. 54°

Recall:

The exterior angle theorem of a triangle states that the measure of an exterior angle equals the sum of the measures of two opposite interior angles of the triangle.

Thus:

In ΔDEF, (8x−2)º is an exterior angle at vertex D.

m∠E = (3x−8)° (interior angle)

m∠F = (4x+13)° (interior angle)

Therefore:

(8x−2)º = (3x−8)° + (4x+13)°

Solve for x

8x - 2 = 3x - 8 + 4x + 13

Combine like terms

8x - 2 = 7x + 5

8x - 7x = 2 + 5

x = 7

Exterior angle at vertex D = (8x−2)º

Plug in the value of x

= 8(7) - 2

= 54º (option D)

Learn more about exterior angle theorem on:

https://brainly.com/question/24756010


Related Questions

LAST ATTEMPT MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)

Answers

Answers:

[tex]I(-2,-1) \to I \ ' \ (-5,-2.5)\\\\J(-1,2) \to J \ ' \ (-2.5,5)\\\\K(2,-1) \to K \ ' \ (5,-2.5)\\\\[/tex]

===============================================

Explanation:

Since the center of dilation is the origin, we multiply each preimage coordinate by 2.5 (which is the scale factor).

For example, the preimage point J(-1, 2) moves to J ' (-2.5, 5)

-1*2.5 = -2.52*2.5 = 5

This will cause the image triangle I'J'K' to be larger than the preimage IJK. Specifically, each side of the image is 2.5 times longer compared to the preimage.

Answer:

i' (-5, -2.5) J' (-2.5, 5) K' (5, -2.5)

Step-by-step explanation:

you just take the original coordinates and multiply them by 2.5

The following stock prices reflect the closing price for the past five days. Find the 3 day SMA
(Simple Moving Average) for days 2-4.
$44.25, $44, $41.75, $40, $39.75

Answers

Answer:

solution

Step-by-step explanation: total=209.75

please help me on this one thx i really need this one.

Answers

Answer:

6 meters

Step-by-step explanation:

Every 7 floors, it goes up by 22.4 meter intervals.

Let's count down,

the 7th floor would be 50.8 - 22.4, which is 28.4.

the 0th floor would be 28.4 - 22.4, which is 6.

Answer:

6

Step-by-step explanation:

Suzie has made a conjecture that the sum of consecutive odd numbers is always a perfect square. The example she used to show this to Timmy is 1 + 3 + 5 + 7+ 16 = 42. However, Timmy was not convinced and made a Venn diagram to find a counter-example, Do you agree with Suzie's conjecture? Use evidence from the Venn diagram to support your response​

Answers

Answer:

Of course you don't agree with Suzie's conjecture - if there is a counterexample (and there is) to a conjecture, that conjecture is false.

Additional note:

Any sum of consecutive odd numbers starting with 1 is a perfect square. It can be proven mathematically, but the pleasant "proof" is to look at actual geometrical squares drawn from unit squares (like in your notebook).

When you have a square of NxN (N^2 unit squares), to go to the next square you need to add N on one side, N on a neighboring side, and 1 to fill the missing unit, for a total of adding 2N+1 squares and ending up with (N+1)x(N+1).

Because you can start from a 1x1 square and then add 2*1+1 = 3 to go to 2x2, then add 2*2+1=5 to go to 3x3 and so on.

Step-by-step explanation:

Timmy is not the brightest person for making this Venn diagram. He just needed to find 1 counterexample.

What is an equation of the line that passes through the points (−3,8) and (-7, 8)

Answers

Answer:

y = 8

Step-by-step explanation:

Since the y- coordinates of the points are equal, both 8 , then

This indicates the line is horizontal and parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through

The line passes through (- 3, 8 ) and (- 7, 8 ) with y- coordinates 8 , then

y = 8 ← equation of line

What is the answer to this?

Answers

Answer:

2x+1=9

Step-by-step explanation:

[tex]\sqrt{2x+1}+5=2[/tex]

[tex]\sqrt{2x+1}=-3[/tex]

[tex]2x+1=9[/tex]

If they want you to solve, then you can go farther.

2x=8

x=4

Check for extraneous solutions:

[tex]\sqrt{2(4)+1} +5 = 2[/tex]

SOMEBODY PLZ HELP NO LINKS PLZ AN THANK YOU
The scatter plot shows the number of minutes people had to wait for service at a restaurant and the number of staff available at he time. A line that models the data is given by the equation y=-1.62x + 18 where y represents the wait time and x represents the number of staff available. Use the equation to make a conjecture about the wait if there are 10 staff members available


A the wait time will be about 18 minutes

B the wait time will be about 5 minutes

C the wait time will be about - 2 minutes

D the wait time will be about 2 minutes

Answers

Answer:

im not too sure but B

Step-by-step explanation:

Express the dollowing fraction in decimal form as a terminating decimal or as a infinite repeating decimal 3/16

Answers

Answer:

3/16 as a decimal is equal to 0.1875.

Let's convert the given fraction to a decimal number.

Explanation:

To convert any fraction to decimal form, we just need to divide its numerator by denominator.

Here the fraction is 3/16 which means we need to perform 3 ÷ 16.

So, 3/16 is equal to 0.1875.

Hope that helps you in some way.

Find the equation for the line bellow

Answers

I don’t really know but I know I see an ex and I did this and it’s multiple-choice I know for sure but if it isn’t you have to say see you’ll get it right I did this helps1+1 is two and I like you

1 1/2 - 1/2 pls helpppppppppp

Answers

Answer:

It would be 1 whole

Step-by-step explanation:

1/2 - 1/2 is 0 the only thing left is one whole

A man buys an article for $600 and sells it for $710. what is his profit or loss

Answers

Answer:

Profit of $110

Step-by-step explanation:

$710-$600=$110

In the rectangular trapezoid ABCD AC is driven by a CD (see figure).
Find the width of the trapezoid if AC = 3, AD = 5.

Answers

Answer:

solution given:

let's see only in a right-angled triangle Δ ACD.

AC=3 units

AD=5 units

since Δ ACD is a right-angled triangle. It satisfies Pythagoras law

[tex]AD^{2}=AC^{2}+CD^{2}[/tex]

25=9+[tex]CD^2[/tex]

[tex]CD^2[/tex]=25-9=16

[tex]CD=\sqrt{16} =4 units[/tex]

Now

Area of rectangle Δ ACD=[tex]\frac{1}{2} CD*AC=\frac{1}{2}*4*3=6\: square \:units[/tex]

similarly,

[tex]\frac{1}{2} AD*CE=6\: square \:units\\ 5*CE=6*2\\CE=\frac{12}{5}=2.4 units[/tex]

since AB=CE=2.4 units

Δ ACE is a right-angled triangle. It satisfies Pythagoras law.

[tex]AC^{2}=AE^{2}+CE^{2}\\3^2=AE^2+2.4^2\\9-5.76=AE^2\\AE and BC=\sqrt{1.24} =1.11 units[/tex]

now

area of trapezoid=area ofΔACD+Area of ΔABC

=6+[tex]\frac{1}{2}AB*BC=6+\frac{1}{2}*2.4*1.11=6+1.33 =7.33\: square \:units[/tex]

simplify 8+2(5-×) thanks​

Answers

Answer:

=8+2(5-x)

=8+10-2x

=18-2x

Answer:

hey am

I think that's be the answer

if you think it's not right

don't write

Quincy feeds his dog 2.75 cups of dog food each day. Each cup of dog food costs $1.25. He multiplies the numbers together to determine how much it costs to feed his dog each day. Which expression will result in the best estimate for Quincy to use to check his multiplication?
2 times 1
2 times 2
3 times 1
3 times 2

Answers

Answer:

3 times 1

Step-by-step explanation:

2.75 - 75 or in other words 7 is closer to 10 than 0, so well round it up to the next number, 3.

1.25 - 25 or in others words 2 is closer to 0 than 10, so we'll round it down to the nearest lowest whole number, 1.

our new expression: 3 × 1. hope that helps!


When Alex went to work the temperature
was -2°F. When he got home from work the
temperature raised 14°. What was the
actual temperature when he got home from
work?

Answers

The actual temperature when he got home from work was 12°F

Luis and Erin are playing a game. They each start with 0 points. At the end of the game, Luis has 250 points, and Erin has -250


Which statement about the game is true?

A. Erin and Luis have a total of 500 points.

B. Erin has lost 250 points.

C. Luis has 250 more points than Erin.

D. Erin and Luis have an equal number of points.

Answers

Answer:

B

Step-by-step explanation:

A birthday cake was cut into equal pieces, and 10 pieces were eaten. The
fraction below shows how much cake was left over. According to the fraction,
into how many pieces was the cake cut?
1
11
A. 1
B. 10
C. 21
O D. 11
TO

Answers

The answer is D, 11.

a.
two more than seven times x
b. the product of ten and f,
increased by one
C. r divided by eleven

Answers

Answer:

A. two more than seven times x7 × x +27x+2B. the product of ten and f increased by one10 × f + 110f+1C. r divided by elevenr ÷ 11

plz answer fast i will mark as brainlist

Answers

Answer:

36 is the answer

Step-by-step explanation:

Hope it will help you

36 Because you have to try to go through the highest numbers like 8 and 9 to get a higher answer so you start at 1 then go to 5, 8, 4, 3, 9 and then 6 to go out.

Hope this helps

Two trucks, A and B, start from the intersection C of two straight roads at the same time. Truck A is traveling twice as fast as truck B, and after 4 hours, the two trucks are 350 miles apart. Find the approximate speed of truck B in miles per hour.


A. 39 B. 51 C. 44 D. 78

Answers

Answer:

6

Step-by-step explanation:

Solve the equation. Express radicals in simplest form.
-4k2 - 13 = -77

Answers

Simply add 13 to both sides and divide by 4, and then square root both sides. Remember, square rooting will give you a positive and negative value for k.

A book store is hosting a special night in which familles can enjoy a story and craft time. Tickets to the event must be bought ahead of time and are $1.50 for children and $2.50 for adults. So far, 45 children's tickets have been sold, which is 60% of the total tickets sold. How many tickets have been sold so far? Show or explain how you got your answer.steps please​

Answers

Answer:

45

Step-by-step explanation:

just typing this so I'll have 20

Three (3) is a common factor of 21 and 22.
O A. True
B. False
SUBMIT

Answers

Answer:

false.

Step-by-step explanation:

Factors for 21: 1, 3, 7, and 21. Factors for 22: 1, 2, 11, and 22.

Answer:

B false

hello hope this helps

Given f(1) = 8 and
f(n) = 3 f(n-1) - 2 then f (4) =

Answers

Answer:

190

Step-by-step explanation:

f(1)=8

f(2)=3f((2-1))-2, f(2)=22

f(3)=3f((3-1))-2, f(3)=64

f(4)=3f((4-1))-2, f(4)=190

The points (8, 1) and (6, 0) fall on a particular line. What is its equation in slope-intercept form?

Answers

y=1/2x-3 i would say

Answer:

y=-3/2 x + 6Step-by-step explanation:

What is the next number
3, 4, 7, 16, 11, 64, …
Answers:
A) 55
B)14
C)39
D)15

Answers

the answer is c) 39 according to the sequence

The next number 3, 4, 7, 16, 11, 64, is: 55.

What is the number pattern?

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.

When all the terms of a geometric sequence are added, then that expression is called geometric series.

We are given the series as;

3, 4, 7, 16, 11, 64, …

If we separate the numbers that in order are in the even place of the odd ones, we would have :

3, 4, 7, 16, 11, 64,..

If we finish in 1 then they increase by 1 in 1, while in 2.- they increase in odd numbers, the following number is: 55

The correct option is A.

Learn more about a number pattern:

brainly.com/question/14471389

#SPJ2

PLEASE HELP!!!
Bob and Sue are 12 miles apart and moving toward each other. Bob is running at a constant speed of 5mph, and Jada walks at a constant speed of 3mph How long does it take until Bob and Sue meet?

Answers

Answer:

34 miles

Step-by-step explanation:

jn

Calculator
6 mm
What is the area of this figure?
6 mm
Enter your answer in the box.
8 mm
8 mm
mm

Answers

Answer:

[tex] {84mm}^{2} [/tex]

Step-by-step explanation:

Area of square= l×l

Area of square= 6mm × 6mn

Area if square = 36 mm²

Area of triangle 1= ½b ×h

Area of triangle 1= ½ (6mm)(8mm)

Area of triangle 1 = 24 mm²

Area of triangle 2 is the same as area of traingle 1 because they have the same base and hight

: . area of triangles is 48mm²

Area of the figure= Area of square + Area of triangles

A of figure = 36+48

A of figure = 84 mm²

Option 2

Use trapezium formula

Area of trapezium= (a+b)/2 * h

a=6 mm (base)

b=8+6=14 mm (Base)

h= 6mm (height)

[tex]area \: of \: trapezium = ( \frac{6 + 14}{2} )(6) \\ = 60mm ^{2} [/tex]

Therefore the area of triangle= 24mm² as calculated in option 1

Area of the figure= Area of trapezium +Area of triangle

Area of figure = 60+24

= 84 mm²

if you multiply the number of cars in the parking lot by 4 there would be 32 cars how many cars are in the lot​?

Answers

If you do the steps backwards 32/4 is 8

Answer:

8

Step-by-step explanation:

there would be 8 cars in the parking lot

What kind of taxes are likely to pay for universities and police?
а
local taxes
b. state taxes
C federal taxes
d income taxes

Answers

Your answer would be B. State Taxes

Answer: I'd say the best answer is b.

Step-by-step explanation:

Other Questions
What channel is the kennedy center honors on tonight? PLEASE!!!! Which option identifies the satellite technology best utilized in the following scenario?A forest management company that is not concerned about time-sensitive problems uses a standardizedinternet satellite mapping system to get a rough sense of the status of wooded areas that are normallyinaccessible to all but skilled hikers. water vapor present in air support water cycle reciprocal of 2 3/11 Consider the following force:A horse is pulling forward on a wagon with a force of 200 N.According to Newton's third law, what other force must be happening?The horse is pushing backward on the wagon with a force of 200 N.The ground is pushing backward on the horse with a force of 200 N.The wagon is pulling backward on the horse with a force of 200 N. Meg visited her Aunt Clare for lunch. After they ate, Aunt Clare made tea. She put the same amount of black tea and milk in both their cups, but Meg decided to add some extra milk to hers. Which cup of tea was darker after they had finished adding milk? One possible theme of call of the wild could be that only the strongest survive. Explain how this relates to darwins theory of natural selection and the survival of the fittest. Do you agree or disagree with this idea? Is there one aspect in which you agree but another with which u do not? please help i only have a few days- untill schools over If 3.31 moles of argon gas occupies a volume of 100 L what volume does 13.15 moles of argon occupy under the same temperature and pressure Can someone please give me the (Answers) to this? ... please ... Will give 10 points.Why does an atom have a neutral charge?A It has equal numbers of electrons and protons.B. The number of neutrons equals the number of protons andelectrons in the atom.C. It has equal numbers of electrons and neutrons.D. It has equal numbers of neutrons and protons. please answer , thank you in advance to whoever does !!!! What type of evidence does Machiavelli use to support his claim that a prince should have no aim other than war and its rules and discipline? logical evidence anecdotal evidence empirical evidence both logical and anecdotal evidence. Read the following passages.Passage 1As the sun began to set, Joanna and her team began to build their snow fortress. Joanna assigned Tucker, Billy, and the other classmates tasks. She announced to the team that she would be the spy. When she made this declaration, Billy rolled his eyes. It seemed as though he disagreed with Joanna taking on the role of leader and spy, but he just got to work. The Hillside team was busy working together to make their fort, which was very large and made of ice and snow. When Joanna saw the enemy's impressive structure, she turned to her team but got a distressed look on her face."Stop! None of you are following my instructions," Joanna cried. "Billy just pushed the walls together, and now there are cracks. If you don't work together and build the fort in the correct way, the whole thing will fall apart.""Don't worry," Tucker replied. "Everything will turn out okay."Tucker looked over at Billy and gave him a gentle smile. Then, Tucker made some holes that could be used for covert operations.Passage 2As the sun began to set, my team and I began to build our snow fortress. I had imagined a simple design that would withstand any attack from the enemy. As the leader, I assigned each individual a task and made myself a spy. Hillside created a massive fort wall made of ice and snow. I turned to my teammates to share my concerns, only to realize that they had failed to follow my instructions. Each person was building a part of the wall in a different manner. Their lack of teamwork and inability to follow directions would make the entire structure fall apart! When I expressed my concerns, Tucker claimed that everything would turn out well. Billy pushed the walls together. Sure enough, fractures formed in the walls. But, Tucker saved the day by creating holes that could be used for covert operations.What is a similarity in the way the authors use point of view in each passage? help What city is the capital of Texas?A)Austin. B)Dallas. C)Santa Fe. D)Sacramento Given that P=x+y.Find P when:x=3 and y=11 The solution of the equation 3 + 5 (t-1) = 33 is ________. Have you read the Shadow and Bone books? Have you seen the show adaptation? Which do you prefer? Explain :) A wastewater manager is concerned about the increasing number of intestinal illnesses in his town and the corresponding increased levels of a pathogenknown to cause this illness found in wastewater samples. Which process should be used to track the source of this waterborne illness in his town?O EpidemiologyO Civil engineeringHydrologic tracingO Water managementHELP ME PLZ A rectangular piece of metal is 25 in longer than it is wide. Squares with sides 5 in long are cut from the four corners and the flaps are folded upwardto form an open box. If the volume of the box is 2730 in3, what were the original dimensions of the piece of metal?What is the original width? in Youve dreaded it for a while, but now you feel prepared. In 30 minutes youll have to terminate tim, a 12-year employee who is beloved by everyone in the firm. Unfortunately, he just hasnt performed very well since his wife died three years ago and while he was given every chance to regain his performance, he has just continued to slide. Which of the following elements of communication is least likely to influence tims perception of your communication effectiveness?.