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WARM UP

WARM UP. (9, 12). (-14, 1). Complementary and Supplementary Angles/ Linear Pairs and Vertical Angles. You can find the complement of an angle that measures x ° by subtracting its measure from 90°, or (90 – x )°.

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WARM UP

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  1. WARM UP (9, 12) (-14, 1)

  2. Complementary and Supplementary Angles/ Linear Pairs and Vertical Angles

  3. You can find the complement of an angle that measures x° by subtracting its measure from 90°, or (90 – x)°. You can find the supplement of an angle that measures x° by subtracting its measure from 180°, or (180 – x)°.

  4. Example 1: Finding the Measures of Complements and Supplements Find the measure of each of the following. A. complement of F (90 - x) 90 – 59 31 B. complement of A if A = (5x - 6) (90 - x) 90 – (5x – 6) 90 – 5x + 6 96 – 5x

  5. C. supplement of Kif K = (7x - 12) (180 - x) 180 – (7x – 12) 180 – 7x + 12 192 – 7x D. G = (7x + 10). Find the supplement of G. (180 - x) 180 – (7x + 10 180 – 7x - 10 170 – 7x

  6. An angle is 10 more than 3 times the measure of its complement. Find the measure of the complement. (90 - x) 90 – (3x + 10) 90 – 3x - 10 80 – 3x

  7. and are supplementary. Find the measure of both angles. and 5x+ 17x – 18 = 180 22x – 18 = 180 22x = 198 x = 9 5(9) 17(9) - 18 45 135

  8. and are complementary. Find the measure of both angles. and 5y + 1 + 3y – 7 = 90 8y – 6 = 90 8y = 96 y = 12 5(12) + 1 3(12) - 7 61 29

  9. IKM or MKI MKL or LKM __________ and __________ are adjacent angles. _______ and ________ form a linear pair. 1 2

  10. W Z V Y X Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent a. YXZ and VXZ Adjacent and form a linear pair b.  YXZ and  WXZ Adjacent b.  VXW and  YXZ None

  11. Linear Pair TheoremIf two angles form a linear pair, then they are supplementary.EX. Find the value of n. 4n + 5 = 8n – 5 -4n = -10 n = 5/2

  12. Vertical angles are the nonadjacent angles formed by two intersecting lines. List all pairs of vertical angles: 4 and 2 1 and  3

  13. Name the pairs of vertical angles. HML and JMK HMJ and LMK

  14. Theorem 2-7-2 Vertical Angles TheoremVertical angles are congruent. Find the measure of each angle in the diagram. 2x + 40 = 5x + 16 24 = 3x x = 8 2x + 40 5x + 16 2(8) + 40 5(8) + 16 56 56

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