Question

In ASTU, SU is extended through point U to point V, m/UST = (x-6)°,

m/TUV = (4x 17)°, and m/STU = (x+7)°. Find m/STU.

Answer 1

∠ STU = 16°

Explanation:

the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠ TUV is an exterior angle of the triangle

∠ UST and ∠ STU are the opposite interior angles , then

∠ TUV = ∠ UST + ∠ STU ( substitute values )

4x - 17 = x - 6 + x + 7 ( simplify right side )

4x - 17 = 2x + 1 ( subtract 2x from both sides )

2x - 17 = 1 ( add 17 to both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Then

∠ STU = x + 7 = 9 + 7 = 16°