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Objectives-What we’ll learn…
• Identify and use adjacent angles and linear pairs of angles.
• Identify and use vertical, complementary and supplementary angles.
Supplementary angles add up to 180º.
60º120º
40º
140º
Adjacent and Supplementary Angles
Supplementary Anglesbut not Adjacent
Complementary angles add up to 90º.
60º
30º40º
50º
Adjacent and Complementary Angles
Complementary Anglesbut not Adjacent
Directions: Identify each pair of angles as
vertical, supplementary, complementary,
or none of the above.
Applications of Complementary and
Supplementary Angles
Let x = the measure of an angle, then = complement of the angle, and = supplement of the angle
90o x180o x
Now let us apply this information.
Example #1
The measure of an angle is 4 times the measure of its complement. Find the measure of the angle and the measure of its complement.
Solution (Method #1)Let x = the measure of the complement.Let 4x = the measure of the angle
x + 4x = 905x = 90
x = 18 (measure of the complement)4x = 72 (measure of the angle)
Example #1
Method #2
Let x = the measure of the angleLet 90 – x – measure of the complement
x = 4(90 – x)x = 360 - 4x5x = 360x = 72 (angle measure)90 – x = 18 (complement measure)
Example #2
The ratio of the complement of an angle to the supplement of the angle is 2:7. Find the measure of the original angle.
Solution:Let x = the angle measureLet 90 – x = measure of the complementLet 180 – x = measure of the supplement
90 2
180 7
x
x