Adjacent Linear Pairs Vertical Supplementary and Complementary Angles

Adjacent, Linear Pairs Vertical, Supplementary, and Complementary Angles

Objectives-What we’ll learn… • Identify and use adjacent angles and linear pairs of angles. • Identify and use vertical, complementary and supplementary angles.

Adjacent angles are “side by side” and share a common ray. 45º 15º

These are examples of adjacent angles. 80º 45º 35º 55º 85º 130º 20º 50º

These angles are NOT adjacent. 100º 50º 35º 55º 45º

Linear pair of angles • two angles that share a vertex form a straight line (add to 180°)

• AEB & BED are a linear pair of angles. They form a straight line & 50+130=180.

When 2 lines intersect, they make vertical angles. 75º 105º 75º

Vertical angles are opposite to one another. 75º 105º 75º

Vertical angles are opposite one another. 75º 105º 75º

Vertical angles are congruent (equal). 150º 30º 150º

Supplementary angles add up to 180º. 40º 120º 60º Adjacent and Supplementary Angles 140º Supplementary Angles but not Adjacent

Complementary angles add up to 90º. 30º 40º 60º Adjacent and Complementary Angles 50º Complementary Angles but not Adjacent

Practice Time!

Directions: Identify each pair of angles as vertical, supplementary, complementary, or none of the above.

#1 120º 60º

#1 120º 60º Supplementary Angles

#2 30º 60º

#2 30º 60º Complementary Angles

#3 75º

#3 Vertical Angles 75º

#4 40º 60º

#4 40º 60º None of the above

#5 60º

#5 60º Vertical Angles

#6 135º 45º

#6 135º 45º Supplementary Angles

#7 25º 65º

#7 25º 65º Complementary Angles

#8 90º 50º

#8 90º 50º None of the above

Directions: Determine the missing angle.

#1 135º 45º

#2 25º 65º

#3 35º

#4 130º 50º

#5 140º

#6 50º 40º

Applications of Complementary and Supplementary Angles Let x = the measure of an angle, then = complement of the angle, and = supplement of the angle 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 4 x = the measure of the angle x + 4 x = 90 5 x = 90 x = 18 (measure of the complement) 4 x = 72 (measure of the angle)

Example #1 Method #2 Let x = the measure of the angle Let 90 – x – measure of the complement x = 4(90 – x) x = 360 - 4 x 5 x = 360 x = 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 measure Let 90 – x = measure of the complement Let 180 – x = measure of the supplement

Example #2 (Continued)