In triangle ABC, angle A is three times greater than angle B and is equal to half of angle C. What is the sum of angles A and B?
1. We take the degree measure ∠B for x, ∠ A = 3x, ∠ C = 6x.
2. Considering that the total value of all internal angles of the triangle is 180 °, we will compose the equation:
3x + 6x + x = 180 °;
10x = 180 °;
x = 18 °;
∠В = 18 °.
∠A = 18 x 3 = 54 °.
∠С = 18 x 6 = 108 °
3. We calculate the total value of ∠А and ∠В:
∠А + ∠В = 54 + 18 = 72 °.
Answer: the total value of ∠А and ∠В is equal to 72 °.
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