SSC CGL 5 Aug 2017 Shift 1 Paper

Question : 68 of 100

Marks: +1, -0

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

Validate

Solution:

According to the question,

∵ PS = QS
∠PST = ∠QST
and TS = TS
∴ ∠PST ≅ ∠QST∴ ∠TPS = ∠TQS = ∠PQR
∴ ∠R + ∠RPT + ∠TPS+ ∠PQR = 180°
⇒ 54° + 46° + ∠PQR+ ∠PQR = 180°
⇒ 2∠PQR = 180° -100°
∴ ∠PQR

= 80°/2=40°

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