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)}`