Answer:
x = 14
Step-by-step explanation:
As shown on the diagram: m∠STU = 8x , m∠RST = 7x - 54
m∠STU + m∠STR = 180
∴ m∠STR = 180 - m∠STU = 180 - 8x
RS ≅ST ⇒ m∠STR = m∠SRT = 180 - 8x
∠STU is exterior angle at U
∴ m∠STU = m∠RST + m∠SRT
∴ 8x = (7x - 54) + (180 - 8x)
Solve for x:
∴ 8x = 7x - 54 + 180 - 8x
∴ 8x = 126 - x
∴ 9x = 126
∴ x = 126/9 = 14
So, the value of x = 14
