Q8 of 34 Page 170

In a triangle ABC, if 2∠A = 3∠B = 6∠C, determine ∠a, ∠B and ∠C.

In a triangle ABC, it is given that


2∠A = 3∠B = 6∠C


⇒ 2∠A = 6∠C


⇒ ∠A = 3∠C


Similarly,3∠B = 6∠C


⇒ ∠B = 2∠C


We know that the sum of the angles of a triangle is 180°.


⇒ ∠A + ∠B + ∠C = 180°


⇒ 3∠C + 2∠C + ∠C = 180°


⇒ 6∠C = 180°


⇒ ∠C = 30°


So, ∠A = 3× ∠C = 90°


∠B = 2× ∠C = 60°


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