Question

Ray QS bisects PQR and mPQR =57°
Find mPQS

Answer 1

The measure of angle ∠PQS is 28.5°

Explanation:

If a ray bisects an angle, then it divides it into two equal angles in measures and the measure of each one is half of the measure of this angle.

In our question

∵ Ray QS bisects ∠PQR

→ That means it divides it into two angles PQS and SQR

∴ m∠PQS = m∠SQR =
`(1)/(2)` m∠PQR

∵ m∠PQR = 57°

→ Multiply its measure by
`(1)/(2)` to find the measures its parts

∴ m∠PQS =
`(1)/(2)` × 57°

∴ m∠PQS = 28.5°

∴ The measure of angle ∠PQS = 28.5°