and are complementary angles. If , find the measure of . Because and are complementary angles, . Substituting 50º for gives

.

Subtracting 50º from both sides, we find that .

and are supplementary angles. If , find the measure of . Because and are supplementary angles, . Substituting 125º for gives

Subtracting 125º from both sides, we find that .

Determine the measures of

Because vertical angles are equal, .

Because adjacent angles add up to 180º, then . We also know . Substituting gives

Subtracting 120º from both sides, we find .

Because and are vertical, they must be equal. Therefore .