Two angles are supplementary. One of them is 18 more than 6 times the other. How large is the larger angle?

Answer 1

Let the two angles be u & v.

we are told that the second angle is "18 more than 6 times the first" which we can express in terms of u as v = 6u + 18 (1)

Since the two angles are supplementary, u + v = 180° (2).

Substitute equation (2) into (1)...

u + v = 180° (1)

u + (6u + 18) = 180

7u + 18° = 180°

7u = 162°

u = 162°/7 = 23¹/₇°

and

v = 6(23¹/₇°) + 18 = 156 ⁶/₇° (the larger of the two angles and thus the desired answer)

Check step: u + v = (23¹/₇°) + (156 ⁶/₇°) = 180°