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 $/angle c$?

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°