Question
What is the value of ∠PQB if PQ ⊥ PB and RS ⊥ AR and RS = PQ, AP = BR?
- 50°
- 40°
- 80°
- 100°
Hint:
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
The correct answer is: 40°
From the figure, In ΔARS, ∠ARS + ∠SAR + ∠SRA = 180° (Angle sum property of triangle)
⇒ 90° + 50° + ∠RSA = 180° (RS ⊥ AR, ∠SRA = 90°)
⇒∠RSA = 40° ————– (i)
Also, AP = BR
⇒ AP + AB = BR + AB
⇒ PB = AR —————– (ii)
In ΔARS and ΔPQB, RS = PQ (given)
∠QPB = ∠SRA = 90°
PB = AR (from ii)
⇒ ΔARS ≅ ΔBQP (SAS congruence criterion)
⇒∠PQB = ∠RSA = 40° (Corresponding parts of congruent triangles
Hence ,the correct option is (b).
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical.
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