Question

10. In a AABC, iſ 2 ZA = 3 ZB = 6 ZC, calculate ZA,ZB and ZC.
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Answer 1

Answer:

∠A , ∠B , ∠C = 90° , 60° , 30°

Step-by-step explanation:

Given,

In a traingle, 2 ∠A = 3∠B = 6∠C .

let 2∠A = 3∠B = 6∠C = k (say)

then, ∠A = k/2 , ∠B = k/3 and ∠C = k/6

We know,

Sum of angles of triangle = 180°

k / 2 + k / 3 + k / 6 = 180

(3k + 2k + k) / 6 = 180

6k / 6 = 180

k = 180°

Then, ∠A = k / 2 = 180 / 2 = 90°

and, ∠B = k / 3 = 180 / 3 = 60°

and, ∠C = k / 6 = 180 / 6 = 30°