PQRS is a parallelogram. m∠Q = 11x + 13 and m∠S = 15x - 23. Find the measure of ∠P.

PQRS is a parallelogram. \(\displaystyle{m}∠{Q}={11}{x}+{13}\) and \(\displaystyle{m}∠{S}={15}{x}-{23}\). Find the measure of \(\displaystyle∠{P}\).

Answers (1)

A parallelogram has opposite angles that are congruent so:
So, \(\displaystyle{m}∠{Q}={11}{\left({9}\right)}+{13}={112}°.\)
A parallelogram has consecutive angles that are supplementary:

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