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1-5 Describing Angle Pair Relationship

1-5 Describing Angle Pair Relationship. Hubarth Geometry. Two angles are complementary ang les if the sum of their measures is 90 o . Each angle is the complement of the other. Two angles are supplementary angles if the sum of their measures

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1-5 Describing Angle Pair Relationship

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  1. 1-5 Describing Angle Pair Relationship Hubarth Geometry

  2. Two angles are complementary angles if the sum of their measures is 90o. Each angle is the complement of the other. Two angles are supplementary angles if the sum of their measures is 1800. Each angle is the supplement of the other. Complementary angles and supplementary angles can be adjacent angles or nonadjacent angles. Adjacent angles are two angles that share a common vertex and side, but have no common interior points Complementary angles Supplementary angles 7 1 3 5 8 6 2 4 Nonadjacent Adjacent Nonadjacent Adjacent

  3. In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles. Because 32°+ 58° = 90°, BACand RSTare complementary angles. Because 122° + 58° = 180°,CADand RSTare supplementary angles. Because BACand CADshare a common vertex and side, theyare adjacent. Ex 1 Identify Complements and Supplements SOLUTION

  4. b.You can draw a diagram with supplementary adjacent angles to illustrate the relationship. a. You can draw a diagram with complementary adjacent angles to illustrate the relationship. Ex 2 Find Measures of a Complement and a Supplement • Given that 1 is a complement of 2 and m1 = 68°, • find m2. b. Given that 3 is a supplement of 4 and m 4=56°, find m3. SOLUTION

  5. Ex 3 Find Angle Measures When viewed from the side, the frame of a ball-return net forms a pair of supplementary angles with the ground. Find mBCEand mECD. (4x + 8)°+ (x +2)°=180° 5x + 10 = 180 5x = 170 The angle measures are144°and36°. x = 34

  6. Angle Pairs Two adjacent angles are a linear pair if their noncommon sides are opposite rays. The angles in a linear pair are supplementary angles. Two angles are vertical angles if their sides form two pairs of opposite rays. 2 4 3 6 1 5

  7. Identify all of the linear pairs and all of the vertical angles in the figure at the right. Ex 4 Identify Angle Pairs SOLUTION

  8. Ex 5 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 The measure of the angles are 30 and 5(30) = 150

  9. 5. Do any of the numbered angles in the diagram below form a linear pair? Which angles are vertical angles? Explain. Practice 1. In the figure, name a pair of complementary angles, a pair of supplementary angles and a pair of adjacent angles 82o 63o 26o, 64o

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