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Question
The exterior angles, obtained on producing the side of a triangle both ways, are 100° and 120°. Find all the angles of the triangle.
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Solution
∠ABP + ∠ABC = 180° ....(Linear pair)
⇒ 100° + ∠ABC = 180°
⇒ ∠ABC = 180° - 100° = 80°
∠ACQ + ∠ACB = 180° ....(Linear pair)
⇒ 120° + ∠ACB = 180°
⇒ ∠ACB = 180° - 120° = 60°
Now, in ΔABC,
∠A + ∠B + ∠C = 180° ....(Angle sum property of a triangle)
⇒ ∠A + 80° + 60° = 180°
⇒ ∠A = 180° - 80° - 60° = 40°
Hence, the angles of a triangle are 40°, 60° and 80°.
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