Two angles are complementary if the sum of their degree measures 90°.
(a) ∠a + ∠b = 90°
∠a and ∠b are complementary angles and they do not have to be adjacent to be complementary.
(b) ∠c + ∠d = 90°
∠c and ∠d are adjacent complementary angles. If adjacent angles are complementary we call them adjacent complementary angles.
Two angles are supplementary if the sum of their degree measures 180°
(a) ∠x + ∠y =180°
∠x and ∠y are supplementary angles.
Angles do not have to be adjacent to be supplementary.
(b) ∠m + ∠n = 180°
∠m and ∠n are adjacent supplementary angles.
If adjacent angles are supplementary angles.
Vertically opposite angles
Look at this ironing board. The legs look like lines intersecting each other forming angles.
Interesting lines from pairs of vertically opposite angles.
∠COA is vertically opposite ∠BOD
∠AOD is vertically opposite ∠COB
On measuring we find ∠COA = 100° and vertically opposite ∠BOD = 100°.
∠AOD = 80° and vertically opposite ∠COB = 80°.