Question

RSTU is an isosceles trapezoid with bases RS and TU. Find x and m/S if m/R=4x +11 and m/T=2x-5.

Answer 1

$\angle R$ and $\angle S$ are supplementary by the same-side interior angles theorem, and $\angle S \cong \angle T$ because of the properties of an isosceles trapezoid, meaning that $\angle R$ and $\angle T$ are supplementary.

$4x+11+2x-5=180\\\\6x+6=180\\\\6x=174\\\\x=\boxed{29}\\\\\implies m\angle S=m\angle T=2(29)-5=\boxed{53^{\circ}}$