[Math] In the three angles, A, B, C of a triangle, angle B exceeds twice angle A by 15 degrees. Express the measure of angle C in terms of angle A.

Question

In the three angles, A, B, C of a triangle, angle B exceeds twice angle A by 15 degrees. Express the measure of angle C in terms of angle A. I know it looks simple, but my reasoning does not agree with the answer in the book. Many of the answers there are incorrect, so I am not sure who is wrong this time around.

Answer 1

We begin by noting that if we have $\triangle ABC$ in Euclidean geometry then we note that:

$$\angle A + \angle B + \angle C = 180^{\circ}$$

Therefore, if we have that $\angle B = 2\angle A + 15^{\circ}$, then:

$$\angle A+2\angle A+15^{\circ}+\angle C=180^{\circ}$$

Rearranging and simplifying we thus have:

$$\angle C = 165^{\circ}-3\angle A$$