Question

In ΔPQR, ∠R = 54°, the perpendicular bisector of PQ at S meets QR at T. If ∠TPR = 46°, then what is the value (in degrees) of ∠PQR?

Answer 1

your answer is as following

/_ PQR = 34°

Answer 2

Given:

the perpendicular bisector of PQ at S meets QR at T.

∠PRQ= 54°

∠TPR = 46°,

Solution:

Using the property of external angles, ∠PTQ = 46° + 54° = 100°

ΔPTS is congruent to ΔQTS, therefore, ∠TPQ = ∠TQP = X

We know, Sum of all angles of a triangle= 180°.

∠PTQ + ∠TPQ + ∠TQP = 180°

100° + X + X = 180°

So, X = 40°

Here, ∠TQP = ∠PQR = 40°