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

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 A C D B A B D C A C D B A B C D

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

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 A B C E D

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

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

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

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

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

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

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

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.

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

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

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

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