Homework 2.1 Vertical Angles, Linear Pairs, Complementary/Supplementary Angles & Angle Bisector Find the complement of each angle. 1. 75° 2. 58° 3. 8° Find the supplement of each angle. 4. 36° 5. 118° 6. 85° Find the missing angle. 7. 8. 155ᵒ
35ᵒ
60ᵒ
Solve for x. 10. 2x + 10 70ᵒ
9. x = 11. x + 30
x = 2x
12. Linear pairs could be defined as being supplementary angles because they always add up to 180º. Are all supplementary angles linear pairs? Explain. uuur
Refer to the diagram to answer each. BE is an angle bisector. 13. If m∠ABC = 86o, find m∠ABE. 14. If m∠ABE = 27°, find m∠EBC. Homework 2.1 Vertical Angles, Linear Pairs, Complementary/Supplementary Angles & Angle Bisector Solutions Find the complement of each angle. 1. 75° 15o 2. 58° 32o 3. 8° 82o Find the supplement of each angle. 4. 36° 144o 5. 118° 62o 6. 85° 95o Find the missing angle. 120o 145o 25o 7. 8. 9. 155ᵒ
35ᵒ
60ᵒ
Solve for x. 10. 2x + 10 70ᵒ
x =50 x = 50 11. x + 30
2x
12. Linear pairs could be defined as being supplementary angles because they always add up to 180º. Are all supplementary angles linear pairs? Explain. No, all supplementary angles are not linear pairs, they will only be linear pairs if they are adjacent supplementary angles as then it will form a straight line/straight angle. uuur
Refer to the diagram to answer each. BE is an angle bisector. 13. If m∠ABC = 86o, find m∠ABE. 43o 14. If m∠ABE = 27°, find m∠EBC. 27o Homework 2.1 Vertical Angles, Linear Pairs, Complementary/Supplementary Angles & Angle Bisector 15. One of two complementary angles is 57° greater than twice its complement. Find the measure of both angles. Solve for the variable(s). 16. 17. x = x = xᵒ (2x – 17)ᵒ (x + 135)ᵒ zᵒ yᵒ y = 48ᵒ
z = 18. 19. x = 105ᵒ x = (2x + 5)ᵒ (3x + 11)ᵒ 20. Given that !" is an angle bisector, Find x if m<2 = 1 + 28x and m<XVW = 59x -­‐1 x = 22. Given that !" is an angle bisector, m <2 =22o, Find m<CAB x = (119 – x)ᵒ 21. Given that !" is an angle bisector, Find m <1, if m<1 = 7x + 7 and m ZVTU= 16x +4 x = 23. Given that !" is an angle bisector, m <2 =30o, Find m<1 x = Homework 2.1 Vertical Angles, Linear Pairs, Complementary/Supplementary Angles & Angle Bisector Solutions 15.One of two complementary angles is 57° greater than twice its complement. Find the measure of both angles. m < 1 = 11o m <2 = 79o Solve for the variable(s). 16. 17. x = 152 x = 48o xᵒ (2x – 17)ᵒ (x + 135)ᵒ zᵒ yᵒ o
y = 132 48ᵒ
z = 132o 18. 19. x = 50 105ᵒ (119 – x)ᵒ x = 27 (2x + 5)ᵒ (3x + 11)ᵒ 20. Given that !" is an angle bisector, Find x if m<2 = 1 + 28x and m<XVW = 59x -­‐1 21. Given that !" is an angle bisector, Find m <1, if m<1 = 7x + 7 and m ZVTU= 16x +4 o
m<1 = 42 x = 1 23. Given that !" is an angle bisector, m <2 =30o, Find m<1 x = 30o 22. Given that !" is an angle bisector, m <2 =22o, Find m<CAB x = 44o