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mathstudent55
The sum of the measures of the angles of a triangle is 180 degrees.

Angles STU and STR are supplementary angles.
Angles R and STR are congruent.

m<STU + m<STR = 180

8x + m<STR = 180

m<STR = 180 - 8x

m<R = m<STR = 180 - 8x

m<RST + m<R + m<STR = 180

7x - 54 + 180 - 8x + 180 - 8x = 180

-9x + 360 = 180

-9x = -126

x = 14
m<STR = 180 - 8x  degrees
also m < SRT = 180-8x ( because side RS = side ST, so isosceles triangle)
So 
7x - 54 + 180 - 8x = 8x  (ext. angle of triangle =sum of opposite internal angles)

7x - 8x - 8x = -180 + 54 = -126
-9x = -126
x = 14 answer

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