Question

Can you help me, please?​

Answer 1

Answer:

a. 18

b.144

c.108

Step-by-step explanation:

Using the given, Angle R equal 5x-54 and Angle T is 8u.

Also RS is congruent to ST. Since SR is congruent to ST, their opposite angles are also congruent using base angle theorem. So angle R is equal to Angle T. However, STU is a exterior angle so STU isn't congruent to SRT.

However, we can add , interior angle T, and STU to 180 to find x.

Interior angle T=SRT so interior angle t=5x-54.

Set up equation

$5x - 54 + 8x = 180$

$13x - 54 = 180$

$13x = 234$

$x = 18$

b.Plug 18 into 8x

$8(18) = 144$

STU=144

c. Using the triangle exterior angle theorem, the exterior angle is equal to the measure of the sum of two non adjacent angles.

Angle S and Angle R are the non adjacent angle to STU.

So we cast up this equation.

$5x - 54 + s = 180$

plug 18 in for x

$5(18) - 54 + s = 144$

$90 - 54 + s = 144$

$36 + s = 144$

s=108