Question

Find the value of x. The diagram is not to scale. Explain your reasoning.

Answer 1

x = 24

Explanation:

Since SR = ST then Δ RST is isosceles, thus the base angles are congruent.

∠ SRT = ∠ STR = 4x - 60

∠ STR and ∠ STU are adjacent and supplementary, thus

∠ STR + ∠ STU = 180, substitute values

4x - 60 + 6x = 180, that is

10x - 60 = 180 ( add 60 to both sides )

10x = 240 ( divide both sides by 10 )

x = 24