1. Angle Relationships Section 1.5 Bridget Jubon and Lauren Ludwikowski

2. Angle Pairs

3. Relationships of Angle Pairs T ●Perpendicular lines form right angles ●Right angles = 90° ●The symbol is for perpendicular lines ● = Not Perpendicular T

4. Assumed: Not Assumed: -Collinearity of points -Betweenness of points -Relative position of points -Straight lines and angles -Congruent segments -Congruent angles -Relative size of segments and angles -Right angles (Perpendicularity) When looking at diagrams...

5. A B C D Opposite Rays E EA and ED are opposite rays EB and EC are opposite rays

6. Finding an Angle’s Complement or Supplement To find an angle’s complement: Subtract the angle from 90° To find an angle’s supplement: Subtract the angle from 180° Note: If an angle is greater than 90° it will not have a complement. Fill in the following table: AngleComplementSupplement 22° 44° 93° X

7. Finding an Angle’s Complement or Supplement Answers: AngleComplementSupplement 22°68°158° 46°44°134° 87°No Compliment93° X°90 - X180 - X

8. Sample Problem A = 2x+8 C = 10x+16 2x+8 = 10x+16 8 = 8x+16 -16 -8 = 8x -1 = x C = 10(-1)+16 = -10+16 = 6°

9. Sample Problem Given: SR TS <T congruent <R Find m<T Steps: 1. Show <S is a right angle 2. Subtract 90° from 180° 3. Divide by 2 T SR T 180°- 90° = 90° 90° 2 = 45° m<T = 45°

10. 2. Add like factors 3. Combine the x’s 4. Divide by 2 Sample Problem X = 52

11. Practice Problem Given: <LOM = 6x <MON = 4x + 4 <LON is a rt. < Find: <MON ● O● O ●L●L ●M●M ● N

12. Practice Problem Given: <LOM = 6x <MON = 4x + 4 <LON is a rt. < Find: <MON Answer: Because <LON is a rt. < it = 90° Set <LOM and <MON equal to 90° 6x + 4x + 4 = 90 Combine like terms 10x + 4 = 90 Subtract 4Final answer: Put 8.6 for x in 4x + 4 10x = 86<MON = 38.4° Divide by 10 x = 8.6 ● O● O ●L●L ●M●M ● N

13. Practice Problem The larger of two supplementary angles is 2 times more than the larger by 6. Find the measure of the larger angle.

14. Practice Problem The larger of two supplementary angles is 2 times more than the larger by 6. Find the measure of the larger angle. Remember: x = angle (smaller) 180-x = supplement (larger) Steps: 1.Set the Supplement equal to the angle 180-x = 2x + 6 2. Combine like terms 174 = 3x 3. Solve for x x = 58 4. Substitute x into the equation 180-58 = 122

15. Practice Problem Given: ZY = XY ZY = 4(ZX) Perimeter of ZXY = 144 Find: ZY X Y Z ~ __

16. Practice Problem Given: ZY = XY ZY = 4(ZX) Perimeter of ZXY = 360 Find: ZY Answer: Add sides together and set equal to 360 4(ZX) + 4(ZX) + (ZX) = 360 Add variables 9(ZX) = 360 Divide by 9 ZX = 40 Substitute 40 for ZX in 4(ZX) to get final answer: ZY = 160 X Y Z ~ __ 4(ZX) (ZX)

17. Works Cited Pricci Packet Sections 1.4 - 1.6 Pricci Powerpoint Section 1.5