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

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

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

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

GUIDED PRACTICE 7. The measure of an angle is twice the measure of its complement. Find the measure of each angle. ANSWER 60°, 30° For Examples 4 and 5