Concept: Describe Angle Pair Relationships Sec 1-5 Concept: Describe Angle Pair Relationships Objective: Given a pair of angles, use special angle relationships to find angle measures.

Example 1 The Alamillo Bridge in Seville, Spain, was designed by Santiago Calatrava. In the bridge, m<1=58° and m<2=24°. Find the supplements of both <1 and <2 Suppl of <1. 180-58 = 122 Suppl of <2: 180 – 24 = 156

Example 2: Find the supplement and complement of each angle A. 38° B. 172° A. Comp: 52° Suppl: 142° B. Comp: none Suppl: 8°

Example 3: Find the measure of each angle <P and <Z are complementary. m<P = 8x - 7 and m<Z = x -11 Make an equation m<P + m<Z = 90 8x-7 + x-11 = 90 9x -18 = 90 +18 +18 9x = 108 X=12 m<P = 8(12)-7 m<P = 89° M<Z= (12)-11 = 1 Now find each angle measure

Example 4: Find the measure of each angle <P and <Z are Supplementary. m<P = 8x + 100 and m<Z = 2x+50 Make an equation m<P + m<Z = 180 8x+100 + 2x+50 = 180 10x+150 = 180 -150 -150 10x = 30 X=3 m<P = 8(3)+100 m<P = 124° M<Z= 2(3)+50 = 56° Now find each angle measure

Example 5 Use the diagram to answer the following questions 2 3 1 4 5 1. Are <1 and <2 a linear pair? Yes 2. Are <4 and <5 a linear pair? NO 3. Are <5 and <3 Vertical angles? 4. Are <1 and <3 vertical <‘s? YES 2 1 5 4 3

Example 6 m<1= 60 m<2 = 60 m<3 = 120 m<4 = 120 <2 = 60°.Find the measure of the other angles m<1= 60 m<2 = 60 m<3 = 120 m<4 = 120 3 1 4 2

Example 7 : Find the measure of m<DEG and m<GEF (12x-7)۫ (7x-3)۫ 7(10)-3 = 67 12(10)-7 =113

Example 8:Find the measure of each angle 4x+15 + 5x+30 = 180 9x+45 = 180 -45 -45 9x = 135 9 X=15 Use Linear Pairs to make and equation Substitute x to find the angles 4x+15 5x+30 3y + 15 3y -15 4(15)+15 = 75 5(15)+30 = 105

Example 8 cont.:Find the measure of each angle 3y+15 + 3y-15 = 180 6y = 180 6 6 y = 30 Use Linear Pairs to make and equation Substitute y to find the angles 4x+15 5x+30 3y + 15 3y -15 3(30)+15 = 105 3(30)-15 = 75

Today's Work

Additional Slides: The following are Terms that you can move and place where you like:

<DOS and <SOG are adjacent angles 2 angles are adjacent if they share a common vertex <DOS and <SOG are adjacent angles D O S G

Vertical Angles 2 angles are vertical angles if their sides form two pairs of opposite rays 1 2 3 4 <1 and <3 are vertical angles <2 and <4 are vertical angles

<5 and <6 are a linear pair 2 adjacent angles are a linear pair if their non-common sides are opposite rays 5 6 <5 and <6 are a linear pair

Two angles are Complementary if the sum of their measures is 90° Complementary Angles Two angles are Complementary if the sum of their measures is 90° 30° 60° 1 2 <1 and <2 are complementary

< 3 and <4 are supplementary Supplementary Angles Two angles are Supplementary if the sum of their measures is 180° 130° 50° 3 4 < 3 and <4 are supplementary