Question

Find the value of x
See picture

Answer 1

x = 14

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