Q. 32

# In figure,   three lines p, q and r are concurrent at O. If a = 50° and b = 90°, find c, d, e and f.

Given: Three coplanar lines AB, CD and PQ meet at O.
∠ BOQ = a = 50° and ∠ BOC = b = 90°
To find: c, d, e and f.
Proof: Adjacent angles, ∠ BOQ, ∠ BOP form a linear pair.
... ∠ BOQ + ∠ BOP = 180° (Linear Pair Axiom)
+ ∠ BOC + ∠ COP = 180°
a + b + c = 180°
50° + 90° + c = 180° (given)
= 180°- (90° + 50°)
= 180° - 140°
= 40°
d = a = 50° (Vertically opp. angles)
e = b = 90° (Vertically opp. angles)
f = c = 40° (Vertically opp. angles).

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