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Question

In a ΔABC, C = 3 B = 2 (A + B). Find the three angles.

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Solution

Given that,

C = 3B = 2(A + B)

3B = 2(A + B)

3B = 2A + 2B

B = 2A

2 AB = 0 … (i)

We know that the sum of the measures of all angles of a triangle is 180. Therefore,

A + B+ C = 180

A + B+ 3 B = 180

A + 4 B = 180 … (ii)

Multiplying equation (i) by 4, we obtain

8 A− 4 B = 0 … (iii)

Adding equations (ii) and (iii), we obtain

9 A = 180

A = 20

Putting the value of A in equation (i), we get

B = 2 A

B = 2 × 20 = 40

C = 3 B = 120

Hence, required angles of triangle is 20, 40, 120


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