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
[tex]5x - 54 + 8x = 180[/tex]
[tex]13x - 54 = 180[/tex]
[tex]13x = 234[/tex]
[tex]x = 18[/tex]
b.Plug 18 into 8x
[tex]8(18) = 144[/tex]
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.
[tex]5x - 54 + s = 180[/tex]
plug 18 in for x
[tex]5(18) - 54 + s = 144[/tex]
[tex]90 - 54 + s = 144[/tex]
[tex]36 + s = 144[/tex]
s=108
