In ΔPQR, QT ⊥ PR and S is a point on QR such that ∠PSQ = p°. If ∠TQR = 46° and ∠SPR = 32°, then the value of p is?
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e. 76°
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Concept |
Understanding |
Application |
Fair calculation |
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Sum of angles of a triangle = 180 Vertically opposite angles are always equal. |
Given ∠PSQ = p ∠TQR = 46° ∠RPS = 32° ∠PTN = 90° Suppose PS and QT intersect each other at N. |
In triangle PNT: ∠PNT = 180 – 90 – 32 = 58° Since ∠PNT and ∠QNS are Vertically opposite angles; ∠QNS = ∠PNT = 58° Now, In triangle QNS: ∠p = 180 – 46 – 58 = 76° |
180 – 90 – 32 = 90 – 32 = 58 180 – 46 – 58 = 180 – 104 = 76 |