Objectives Angle Pair Relationships Adjacent Angles Vertical Angles

Objectives Angle Pair Relationships ◦ Adjacent Angles ◦ Vertical Angles ◦ Linear Pair ◦ Complementary Angles ◦ 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

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

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

Vertical angles are congruent 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

Linear Pair Two adjacent angles (common vertex and a common ray) that form a straight line. So the two angles add up to ? 180

Practice Time!

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

#1 120º 60º Supplementary Angles And a Linear Pair

#2 30º 60º Complementary Angles

#3 Vertical Angles 75º

#4 40º 60º None of the above

#5 60º Vertical Angles

#6 135º 45º Supplementary Angles and a Linear Pair

#7 25º 65º Complementary Angles

#8 90º 50º None of the above

Directions: Determine the missing angle.

#1 135º 45º

#2 65º

#2 25º 65º

#3 35º

#4 130º 50º

#5 ? 140º

#5 140º

#6 Rectangle ? 40º

#6 Rectangle 50º 40º

EXAMPLE ALGEBRA Find angle measures in a linear pair Two angles form a linear pair. The measure of one angle is 5 times the measure of the other. Find the measure of each angle. SOLUTION Let x° be the measure of one angle. The measure of the other angle is 5 x°. Then use the fact that the angles of a linear pair are supplementary to write an equation.

EXAMPLE Find angle measures in a linear pair x + 5 x = 180° 6 x = 180° x = 30° Write an equation. Combine like terms. Divide each side by 6. ANSWER The measures of the angles are 30° and 5(30)° = 150°.