In a triangle, ABC, ∠A = 70°, ∠B = 80° and D is the incentre of ΔABC. ∠ACB = 2x° and ∠BOC = y°. The values of (x + y), respectively are:
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Correct answer: B
Explanation
The correct answer is Option 2 i.e. 140°.
In a triangle ABC:
∠A = 70°, ∠B = 80°
D is the incentre of ΔABC.
∠ACB = 2x° and ∠BDC = y°
In ΔABC,
∠A + ∠B + ∠C = 180°
⇒ 70 + 80 + ∠C = 180°
⇒ ∠C = 180 – 150 = 30°
∠ACB = 30°
⇒ 2x = 30°
⇒ x = 15°
Since D is incentre of the triangle;
∠BDC = y = (90 + ∠BAC/2) = (90 + 35) = 125°
Value of (x + y) = 15 + 125 = 140°