Question

Quadrilateral PQRS is a parallelogram. If m angle P=72°, then find m angle Q and m angle R

Answer 1

m∠Q = 108°

m∠R = 72°

Explanation:

In a parallelogram, adjacent angles are supplementary, meaning their measures add up to 180°.

In parallelogram PQRS, angles P and Q are adjacent. Therefore, if the measure of angle P is 72°, we can calculate the measure of angle Q as follows:

`\begin{aligned}m\angle P + m\angle Q &= 180^(\circ)\\72^(\circ) + m\angle Q &= 180^(\circ)\\72^(\circ) + m\angle Q - 72^(\circ) &= 180^(\circ) - 72^(\circ)\\m\angle Q &= 108^(\circ)\end{aligned}`

Therefore, the measure of angle Q is 108°.

In a parallelogram, opposite angles are congruent. Therefore, as angle R is opposite angle P, and angle S is opposite angle Q:

`m\angle R = m\angle P = 72^(\circ)`

`m\angle S = m\angle Q = 108^(\circ)`

Therefore, the measure of angle R is 72°.