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- 1. Angles Pair Relationships Objectives: - Identify vertical angles and linear pairs - Identify complementary and supplementary angles
- 2. Vertical Angles <ul><li>Two angles are vertical angles if their sides form 2 pairs of opposite rays. </li></ul><ul><li>Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles. </li></ul>4 1 3 2
- 3. Linear Pairs <ul><li>Two adjacent angles are a linear pair if their noncommon sides are opposite rays. </li></ul><ul><li>Angles 5 and 6 are a linear pair </li></ul>5 6
- 4. Vertical Angles <ul><li>Solve for x and y. Then find the angle measures. </li></ul><ul><li>(3x + 5) + (x + 15) = 180 </li></ul><ul><li>4x + 20 = 180 </li></ul><ul><li>4x = 160 </li></ul><ul><li>X = 40 </li></ul>y + 20 3x + 5 4y - 15 x + 15 All numbers are in degrees
- 5. Vertical Angles <ul><li>Solve for x and y. Then find the angle measures. </li></ul><ul><li>(y + 20) + (4y - 15) = 180 </li></ul><ul><li>5y + 5 = 180 </li></ul><ul><li>5y = 175 </li></ul><ul><li>y = 35 </li></ul>y + 20 3x + 5 4y - 15 x + 15 All numbers are in degrees
- 6. Vertical Angles <ul><li>Solve for x and y. Then find the angle measures. </li></ul><ul><li>3x + 5 = 3*40 + 5 = 125 </li></ul><ul><li>X + 15 = 40 + 15 = 55 </li></ul><ul><li>Y + 20 = 35 + 20 = 55 </li></ul><ul><li>4y - 15 = 4*35 - 15 = 125 </li></ul><ul><li>The vertical angles are congruent </li></ul>y + 20 3x + 5 4y - 15 x + 15 All numbers are in degrees
- 7. Complementary & Supplementary Angles <ul><li>Two angles are complementary if the sum of their measures is 90º. </li></ul><ul><li>Each angle is the complement of the other. </li></ul><ul><li>Two angles are supplementary if the sum of their measures is 180º. </li></ul><ul><li>Each angle is the supplement of the other. </li></ul>
- 8. Complementary & Supplementary Angles <ul><li>Complementary and supplementary angles can be adjacent or nonadjacent </li></ul><ul><li>Draw 2 angles that are complementary adjacent. </li></ul><ul><li>Draw 2 angles that are complementary nonadjacent. </li></ul><ul><li>Draw 2 angles that are supplementary adjacent. </li></ul><ul><li>Draw 2 angles that are supplementary nonadjacent. </li></ul>
- 9. Complementary & Supplementary Angles <ul><li>If Angle A and Angle C are complements, and Angle A measures 57 degrees, what does Angle C measure? </li></ul><ul><li>If Angle R and Angle Q are supplements, and Angle R measures 47 degrees, what does Angle Q measure? </li></ul><ul><li>If Angle W and Angle Z are complementary, and the measure of Angle Z is five times the measure of angle W, what is the measure of Angle W? </li></ul>
- 10. Do page 47 4-27 <ul><li>Homework: worksheets </li></ul>

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