Question

In triangle $abc$, the measure of $\angle a$ is $86$ degrees. the measure of $\angle b$ is $22$ degrees more than three times the measure of $\angle c$. what is the measure, in degrees, of $\angle c$?

Answer 1

Given:
m∠A = 86°

Because the measure of angle B is 22 degrees more than three times the measure of angle C, therefore
m∠B = 3*m∠C + 22                 (1)

The sum of the angles should be 180°, therefore
m∠A + m∠B + m∠C = 180       (2)

Note that m∠A = 86°
Substitute equation (1) for m∠B in equation (2) to obtain.
86 + (3*m∠C + 22) + m∠C = 180
86 + 3*m∠C + 22 + m∠C = 180
4*m∠C = 180 - 86 - 22 = 72
m∠C = 72/4 = 18°

Answer:  m∠C = 18°