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1.6

1.6. Angle Pair Relationships. 1. 2. GOAL. GOAL. Identify vertical angles and linear pairs. Identify complementary and supplementary angles. To solve real-life problems, such as finding the measures of angles formed by the cables of a bridge. What you should learn.

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1.6

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  1. 1.6 Angle Pair Relationships 1 2 GOAL GOAL Identify vertical angles and linear pairs. Identify complementary and supplementary angles. To solve real-life problems, such as finding the measures of angles formed by the cables of a bridge. Whatyou should learn Why you should learn it

  2. 1.6 Angle Pair Relationships VERTICAL ANGLES AND LINEAR PAIRS 1 GOAL 1 4 2 3 Vocabulary Two angles whose sides form two pairs of opposite rays are called _____________. vertical angles Identify the pairs of vertical angles in the diagram. Click to check.

  3. common side 5 6 noncommon sides are a linear pair. EXAMPLE 1 Two adjacent angles whose noncommon sides are opposite rays are called a _________. linear pair

  4. 2 3 1 4 5 • Are a linear pair? • b. Are a linear pair? • c. Are vertical angles? • d. Are vertical angles? • Click to see the answers. EXAMPLE 2 Extra Example 1 yes no no yes

  5. Columbus Avenue 36° Main Street EXAMPLE 3 Extra Example 2 In one town, Main Street and Columbus Avenue intersect to form an angle of 36°. Find the measures of the other three angles. Click to see a diagram. Click to see the answers.

  6. M P L N O Extra Example 3 Solve for x and y. Then find the angle measures. Click for a hint. Solve each equation to find x and y. Click for the answers.

  7. J K H I G 2. What is the measure of Checkpoint 1. Name one pair of vertical angles and one pair of angles that form a linear pair. Click to see the answers. Vertical angle pairs: Linear pairs:

  8. 1.6 Angle Pair Relationships COMPLEMENTARY AND SUPPLEMENTARY ANGLES 2 GOAL are now nonadjacent complementary angles. 1 2 Vocabulary If the sum of the measures of two angles is 90°, the angles are ______________ angles, and each is the ___________ of the other. complementary complement Note: Complementary angles may or may not be adjacent.

  9. Note: Supplementary angles may or may not be adjacent. If are adjacent and supplementary, they form a _________. 3 4 are now nonadjacent supplementary angles, and they no longer form a linear pair. EXAMPLE 4 If the sum of the measures of two angles is 180°, the angles are _____________ angles, and each is the ___________ of the other. supplementary supplement linear pair

  10. EXAMPLE 5 Extra Example 4 State whether the two angles are complementary, supplementary, or neither. Click for the solution. neither 12 12 supplementary 9 3 9 3 neither 6 6

  11. Given that is a supplement of find Click to see the solution. Click to see the solution. • Given that is a complement of find EXAMPLE 6 Extra Example 5

  12. are supplementary. The measure of is half the measure of Find Click for a hint. Substitute and solve. Click for the solution. Extra Example 6

  13. are complements and are supplements. If is four times find the measure of each of the three angles. Click for a hint. Substitute and solve. Click for the answers. Checkpoint

  14. QUESTIONS?

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