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32 votes
32 votes
The angles of a triangle are A, B and C.

Angle A is three times as big as angle B.
Angle B is half the size of angle C.
What is the size of angle A?

User Rjv
by
2.5k points

1 Answer

21 votes
21 votes

Answer:

∠A = 90°

Explanation:

∠A = 3∠B

∠B = 1/2 × (∠C), this can also be written as ∠C = 2∠B

∠A + ∠B + ∠C = 180, because there are 180° inside a triangle

Write angle A, B and C in terms of angle B:

3 ∠B + ∠B + 2 ∠B = 180

Simplify:

6 ∠B = 180

∠B = 180 ÷ 6 = 30°

Work out angle A:

∠A = 3∠B = 3 × 30°

∠A = 90°

User Joe Generic
by
2.7k points