1.1.4 Pairs of Angles (continued) Example 2 Finding the Measure of Complements and Supplements The relationship between adjacent angles is based on the position of the angles. There are also special relationships between angles based on their measures. Complementary and supplementary angles are pairs of angles that are related to each other by their measures. Complementary angles are two angles whose measures have a sum of 90°. So, the complement of an angle can be found by subtracting its measure from 90°. Supplementary angles are two angles whose measures have a sum of 180°. So, the supplement of an angle can be found by subtracting its measure from 180°.
The measure of ∠ M is given in the figure. m ∠ M = 37.2°
The complement of an angle is found by subtracting the measure of the angle from 90°. So, the measure of the complement of ∠ M is 90° − 37.2°, or 52.8°. You can check your work by adding the angles. If the sum of two angles is equal to 90°, then the angles are complementary. 37.2° + 52.8° = 90° So, the angles are complementary and 52.8° is the complement of 37.2°. An expression for the measure of ∠ N is given in the figure. m ∠ N = (5 x + 49)° The supplement of an angle is found by subtracting the measure of the angle from 180°. So, the measure of the supplement of ∠ N is 180° − (5 x + 49)°, or (131 − 5 x )°. Add the expressions for the two angles to confirm that they are supplementary angles. The sum is 180°, so the angles are supplementary.
Example 3 Applying Complements and Supplements If x ° is the measure of an angle, then the measure of that angle’s complement can be represented by the expression (90 − x )°. Similarly, the angle’s supplement can be represented by the expression (180 − x )°.
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