In the figure, in ΔPQR, PT is perpendicular to QR at T and PS is the bisector of ∠QPR. If ∠PQR = 78º, and ∠TPS = 24º, then the measure of ∠PRQ is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 30º
Here ∠PQR = 78º, and ∠TPS = 24º
In Δ PTQ
∠P = 180° - ( 78° + 90° ) = 12°
⇒ ∠QPS = 12 ° + 24° = 36°
Since PS is the angle bisector so ∠RPS = 36°
Total angle P = 36° + 36° = 72°
And ∠Q = 78°
so in ΔPQR
∠P + ∠Q + ∠R = 180°
72° + 78° + ∠R = 180°
∠R = 30°