Question

Diagonals of a parallelogram PQRS intersect at O. If ∠QOR = 90° and ∠PRQ = 70°, then find the measure of ∠OPQ.

Answer 1

The measure of ∠OPQ = 70°

GIVEN

PQRS is a parallelogram

∠QOR = 90°

∠PRQ = 70°

TO FIND

Measure of ∠OPQ

SOLUTION

We can simply solve the above problem as follows;

It is given

PQRS is parallelogram

∠QOR = 90°

∠PRQ = 70°

We know that opposite angles of a parallelogram are equal in measurement.

So,

∠P = ∠R

We know that diagonals of a parallelograms are also angle bisectors of its angles

Therefore,

∠P/2 = ∠R/2 = 70°

Hence, The measure of ∠OPQ = 70°

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