PROOF Julita works for a company that makes lounge chairs. As shown in the figure, the back of each chair is an isosceles triangle that can be adjusted so the person sitting on the chair can recline.

Suppose the chair is adjusted so m∠Q=50°.
What is m∠QRS?
Write a paragraph proof to justify your argument.

____°; Because △PQR
is isosceles, base angles are congruent, so m∠P=
m∠

. It is given that m∠Q=50°,
so by the Triangle Angle-Sum Theorem, m∠P+m∠QRP+

° =180°.
By substitution, 2m∠QRP+

°=180°
. 2m∠QRP=

°, so m∠QRP=

°. Because ∠QRP
and ∠

are supplementary, m∠QRS=180° −

° =

°.