Question

A point P is to be marked on AB and a line PQ drawn such that the measures of ∠APQ and ∠BPQ are in the ratio 4 : 5. What should be ∠APQ?

Answer 1

We know that the sum of the angles in a linear pair is 180°.

∠APQ and ∠BPQ form a linear pair.

⇒ ∠APQ + ∠BPQ = 180°

Ratio of the measures of ∠APQ to ∠ BPQ = 4 : 5

Measure of ∠APQ = 180° × = 80°