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1.4 Exploring Angle Pairs

1.4 Exploring Angle Pairs. Objectives: The Student Will … Identify and use special pairs of angles. Use special angle pairs to determine angle measure. C. D. A. A. C. C. C. D. B. B. A. D. D. A. B. B. Adjacent Angles. Two coplanar angles. Have a common vertex.

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1.4 Exploring Angle Pairs

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  1. 1.4 Exploring Angle Pairs Objectives: The Student Will … • Identify and use special pairs of angles. • Use special angle pairs to determine angle measure.

  2. C D A A C C C D B B A D D A B B Adjacent Angles • Two coplanar angles • Have a common vertex • Have a common side, but no common interior points. Examples: ∡ABC and ∡CBD Nonexamples: ∡ABC and ∡ABD ∡ABC and ∡BCD

  3. Y N J Z A O X B K M L D C V W Are they Adjacent or Not??? ADB, BDC OKN, MJL WVX, XVZ

  4. A B D E C Vertical Angles • Are two nonadjacent angles • Formed by two intersecting lines • Think of a bow tie • For every set of intersecting lines there are two sets of congruent angles Examples: ∡AEB and ∡CED, ∡AED and ∡BEC

  5. X W V Y Z G H I E F J Are they Vertical or Not??? EFG, GFH YVZ, WVX IHJ, EHJ YVZ, ZVW XVY, WVZ ZVW, WVX

  6. P Y Q 50° 1 40° R X 2 Z Complementary Angles • Two angles whose measures have a sum of 90 • Examples: 1 and 2 are complementary PQR and XYZ are complementary

  7. 53 37 Example of Complimentary Angles 15 60 ? 75

  8. H M 100° N 80° E F G Supplementary Angles • Two angles whose measures have a sum of 180 • Example: EFH and HFG are supplementary M and N are supplementary

  9. Examples of Supplementary Angles 130 50 45 135

  10. B Common Side C Noncommon Sides Are oppositerays “straight line” E D Linear Pair • Whose noncommon sides are opposite rays • The angles of a linear pair forms a straight line • Is a pair of adjacent angles Example: ∡BED and ∡BEC

  11. G H I E F J Are they a Linear Pair or Not??? Z W X EFG, GFH Y YXZ, WXZ IHJ, EHJ YXW, WXZ EFG, IHJ

  12. Example 1: Refer to the figure below. Name an angle pair that satisfies each condition. a.) two angles that form a linear pair. b.) two acute vertical angles.

  13. (2x + 24)° (4x + 36)° Example 2: Since ∡KPL and ∡JPL are a linear pair, then we know their sum is 180° ∡KPL and ∡JPL are a linear pair, m∡KPL = 2x + 24, m∡4x + 36. What are the measures of ∡KPL and ∡JPL? m∡KPL + m∡JPL = 180° (2x + 24) + (4x + 36) = 180° 6x + 60 = 180° m∡KPL = 2(20) + 24 = 64° - 60 - 60 6x = 120° m∡JPL = 4(20) + 36 = 116° 6x = 120° 6 6 x = 20°

  14. Example: If PQ is the angle bisector of RPS, then RPQQPS Q R S P Angle Bisector • A ray that divides an angle into two congruent angles

  15. W A B Angle Bisector X Z D Y C Examples 3: If mYZX = 20, If mADB = 35, then mWZX = ___ 20 35 then mBDC = ___ then mWZY = ___ 40 70 then mADC = ___

  16. If BX bisects ABC, find x and mABX and mCBX. X A 3x + 5 2x + 30 B C Example 4: Bisector cuts and angle into two equal parts. Then m∡ABX = m∡CBX m∡ABX = m∡CBX 3x + 5 = 2x + 30 -2x -2x x + 5 = 30 - 5 -5 x = 25 m∡ABX = 3(25) + 5 = 80° m∡CBX = 2(25) + 30 = 80°

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