EXAMPLE 4 Identify angle pairs Identify all of

EXAMPLE 4 Identify angle pairs Identify all of the linear pairs and all of the vertical angles in the figure at the right. SOLUTION To find vertical angles, look or angles formed by intersecting lines. ANSWER 1 and 5 are vertical angles. To find linear pairs, look for adjacent angles whose noncommon sides are opposite rays. ANSWER 1 and 4 are a linear pair. are also a linear pair. 4 and 5

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

GUIDED PRACTICE 6. For Examples 4 and 5 Do any of the numbered angles in the diagram below form a linear pair? Which angles are vertical angles? Explain. ANSWER No, adjacent angles have their non common sides as opposite rays, 1 and 4 , 2 and 3 and 6, these pairs of angles have sides that from two pairs of opposite rays 5,

GUIDED PRACTICE For Examples 4 and 5 7. The measure of an angle is twice the measure of its complement. Find the measure of each angle. SOLUTION Let x° be the measure of one angle. The measure of the other angle is 2 x° then use the fact that the angles and their complement are complementary to write an equation x° + 2 x° = 90° Write an equation 3 x = 90 Combine like terms x = 30 Divide each side by 3 ANSWER The measure of the angles are 30° and 2( 30 )° = 60°