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

Question
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)

2021-01-09
A parallelogram has opposite angles that are congruent so:
\(\displaystyle∠{Q}≅∠{S}\)
\(\displaystyle{m}∠{Q}={m}∠{S}\)
11x+13=15x−23
11x=15x−36
−4x=−36
x=9
So, \(\displaystyle{m}∠{Q}={11}{\left({9}\right)}+{13}={112}°.\)
A parallelogram has consecutive angles that are supplementary:
\(\displaystyle{m}∠{P}+{m}∠{Q}={180}°\)
\(\displaystyle{m}∠{P}+{112}°={180}°\)
\(\displaystyle{m}∠{P}={68}°\)
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