How to do angle relationships

1. Complementary Angles

Complementary angles are two positive angles whose sum is 90 degrees. For example, complementary angles can be adjacent, as seen in with ∠ABD and ∠CBD in the image below. Or they can be two acute angles, like ∠MNP and ∠EFG, whose sum is equal to 90 degrees. Both of these graphics represent pairs of complementary angles.

2. Supplementary Angles are two positive angles whose sum is 180 degrees. For example, supplementary angles may be adjacent, as seen in with ∠ABD and ∠CBD in the image below. Or they can be two angles, like ∠MNP and ∠KLR, whose sum is equal to 180 degrees. Both of these graphics represent pairs of supplementary angles.

3. Adjacent angles are two angles in a plane that have a common vertex and a common side but no common interior points. Angles 1 and 2 are adjacent angles because they share a common side.

4. Vertical angles are two nonadjacent angles formed by two intersecting lines or opposite rays. Think of the letter X. These two intersecting lines form two sets of vertical angles (opposite angles). And more importantly, these vertical angles are congruent. In the accompanying graphic, we see two intersecting lines, where ∠1 and ∠3 are vertical angles and are congruent. And ∠2 and ∠4 are vertical angles and are also congruent.

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