In a ΔPQR, R = 62°. The perpendicular bisector of PQ meets QR at T. If ∠TPR = 38°. What is the measure of ∠PQR?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 40°.
T lies on QR, and TP = TQ (since T is on the perpendicular bisector)
So, ΔPTQ is isosceles with TP = TQ ⇒ ∠TPQ = ∠PQT
Let ∠PQR = y, ∠QPR = x
x + y + 62° = 180° ⇒ x + y = 118° …(1)
∠TPQ = ∠PQT = y
∠QPR = ∠QPT + ∠TPR = x
⇒ x = y + ∠TPR = y + 38°
From (1): (y + 38°) + y = 118°
⇒ 2y = 80°
⇒ y = 40°