PQ and PR of △PQR are produced to points S and T, respectively. The bisectors of ∠SQR and ∠TRQ meet at U. If ∠QUR = 59°, then the measure of ∠P is :
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 62°.
Given,
∠QUR = 59°
We know that,
If the bisectors of ∠SQR and ∠TRQ meet at U, then
⇒ ∠QUR = 90°- ∠P/2
⇒ 59° = 90°- ∠P/2
⇒ ∠P/2 = 90 - 59 = 31°
⇒ ∠P = 31° × 2 = 62°