Ask question

Ask question

All categories

3 years ago

9

An exterior angle of a triangle is 152°. If the non-adjacent angles are congruent, then what are the measures of all of the inte

rior angles of the triangle?
a. 62°, 59°, 59°
b. 90°, 45°, 45°
c. 152°, 14°, 14°
d. 28°, 76°, 76°

1 answer:

nevsk [136]3 years ago

5 0

9514 1404 393

Answer:

d. 28°, 76°, 76°

Step-by-step explanation:

The sum of the "non-adjacent" interior angles of the triangle is equal to the exterior angle, so is 152°. If those angles are congruent, each is half of 152°, or 76°. The remaining angle is the supplement to 152°, so is 180-152 = 28 degrees.

The interior angles are 28°, 76°, 76°.

You might be interested in

Is TAG BAG? IF so, identif th similarity postulate or theorem that applies

kodGreya [7K]

Step 1

Given;

$Triangle\text{ TAG \textasciitilde Triangle BAG}$

Required; To find the similarity postulate or theorem that applies.

Step 2

Both triangles share one side AG

They also have a common angle;

$90^o$

Side AG = 10 units and ∠AGT ≅ ∠AGB.

Thus, options A and B are discarded.

Step 3

Now, as for the SAS criteria, we need two sides to be congruent and their included angles to be congruent.

But, as no other information is given, we cannot determine whether the given triangles are congruent or not.

Therefore, the answer is; Option D

$cannot\text{ be determined}$

4 0

1 year ago

Please solve this for me using substitution

Vinvika [58]

<h2> <u>Explanation</u><u>:</u></h2>

$\bf \underline{★Given-} \\$

$\textsf{4x + 5y = 8};$

$\textsf{5x + 4y = 12}$

$\bf \underline{★To\: find-} \\$

$\textsf{the value of x and y in equation?}$

$\bf \underline{★Solution-} \\$

$\sf \leadsto 4x + 5y = 8 - - - (i)$

$\sf \leadsto 5x + 4y = 12 - - - (ii)$

By first equation,

$\sf \leadsto 4x + 5y = 8$

$\sf \leadsto 4x = 8 - 5y$

$\sf \leadsto x = \dfrac{8 - 5y}{4}$

$\textsf{Now, we can find the original value of Y.}\\$

$\sf \leadsto 5x + 4y = 12$

$\sf \leadsto 5 \bigg( \dfrac{8 - 5y}{4} \bigg) + 4y = 12$

$\sf \leadsto \dfrac{40 - 25y}{4} + 4y = 12$

$\sf \leadsto \dfrac{40 - 25y + 16y}{4} = 12$

$\sf \leadsto \dfrac{40 - 9y}{4} = 12$

$\sf \leadsto 40 - 9y = 12(4)$

$\sf \leadsto 40 - 9y = 48$

$\sf \leadsto -9y = 48 - 40$

$\sf \leadsto -9y = 8$

$\sf \leadsto y = \dfrac{ -8}{9}$

$\textsf{Now, we can find the original value of X.}\\$

$\sf \leadsto 4x + 5y = 8$

$\sf \leadsto 4x + 5 \bigg( \dfrac{ -8}{9} \bigg) = 8$

$\sf \leadsto 4x - \dfrac{40}{9} = 8$

$\sf \leadsto \dfrac{36x - 40}{9} = 8$

$\sf \leadsto 36x - 40 = 8(9)$

$\sf \leadsto 36x - 40 = 72$

$\sf \leadsto 36x = 72 + 40$

$\sf \leadsto 36x = 112$

$\sf \leadsto x = \dfrac{112}{36}$

$\underline{\textsf{Answer-}}\\$

Therefore, the values of x and y are -8/9 and 112/36 respectively.

6 0

2 years ago

Y’all please give me the answer to this. (7 questions) have to show work.Geometry. Will mark brainliest.

topjm [15]

Answer:

Step-by-step explanation:

Sweet. Get to answer finally. I was the guy commenting on your other post.

1. 72

2. 46

3. 99

4. Same side interior angles are supplementary

5. alternate interior angles are equal to each other so set up the x expressions equal to each other. 5x-7=3x+17. Solve for x

5x-7=3x+17

2x=24

x=12

plug it in for the 5x-7 and get an angle.. 5(12)-7

60-7

53.

The 5x-7 and the 4y+3 is supplementary.

so 53+3+4y=180. combine the 2 and set them equal to 180 to find y

56+4y=180

124=4y

y=31

And now we find the angle of 6. We know that corresponding angles are equal and the y expression and angle 6 are corresponding angles

so plug in your answer for y in the expression..

4(31)+3 = 127.

so angle 6 is 127

6 0

3 years ago

A bank requires a borrower to pay 1 ½ points for a loan. Find the amount of the loan origination fee for a loan of $89,000.

mezya [45]

0.015×89,000
=1,335
..................

5 0

3 years ago

Factor the following expressions completely. Show and check all work on your own paper.

Katyanochek1 [597]

5x2 would be 10 and 10-50x would be negative 40x and 40x + 125 would be 165x

5 0

3 years ago