Angle Pairs

1. Angle Pairs

2. Complementary Angles Complementary angles are two angles whose measures have a sum of 90°.

3. Complementary Angles These two angles (40° and 50 °) are complementary because they add up to 90 °. But the angles don't have to be together. These two are complementary because 27 ° + 63° = 90 °.

4. Given that the two angles below are complementary, solve for the value of x and the angle measurements. m A  30 m B  2x + 10 m A + m B 30 + 2x + 10 2x 2x x 90 90 90 – 30 – 10 50 25 = = = = =  30°  60°

5. Given that the two angles below are complementary, solve for the value of x and the angle measurements. m C  2x + 20 m D  3x – 5 m C + m D 2x + 20 + 3x – 5 2x + 3x 5x x 90 90 90 – 20 + 5 75 15 = = = = =  50°  40°

6. Given that the two angles below are complementary, solve for the value of x and the angle measurements. m FEG  35 – x m GEH  45 + 2x m FEG + m GEH 35 – x + 45 + 2x – x + 2x x 90 90 90 – 35 – 45 10 = = = =  25°  65°

7. Solve for the value of x and the measurements of the angles, given that each pair of angles are complementary. J = (5x – 18)° & K = (4x)° L = (45 – 2x)° & M = (40 + 3x)° NOP = (5x – 20) & POQ = (x – 10)° 1 = (45 – x)° & 2 = (2x + 15)° R = x° & S = (2x + 6) °

8. Solve for the value of x and the measurements of the angles, given that each pair of angles are complementary. J = (5x – 18)° & K = (4x)° 12 42 48 L = (45 – 2x)° & M = (40 + 3x)° 5 35 55 NOP = (5x – 20) & POQ = (x – 10)° 20 80 10 1 = (45 – x)° & 2 = (2x + 15)° 30 15 75 R = x° & S = (2x + 6) ° 28 28 62

9. Supplementary Angles Supplementary angles are two angles whose measures have a sum of 180°.

10. Supplementary Angles These two angles (140 ° and 40°) are supplementary because they add up to 180°. But the angles don't have to be together. These two are supplementary because 27 ° + 63° = 180°.

11. Given that the two angles below are supplementary, solve for the value of x and the angle measurements. m T  50 m V  3x + 40 m T + m V 50 + 3x + 40 3x 3x X 180 180 180 – 50 – 40 90 30 = = = = =  50°  130°

12. Given that the two angles below are supplementary, solve for the value of x and the angle measurements. m W  3x – 55 m X  155 – x m W + m X 3x – 55 + 155 – x 3x – x 2x x 180 180 180 + 55 – 155 80 40 = = = = =  65°  115°

13. Given that the two angles below are supplementary, solve for the value of x and the angle measurements. m BYA  3x + 5 m AYZ  2x m BYA + m AYZ 3x + 5 + 2x 3x + 2x 5x x 180 180 180 – 5 175 35 = = = = =  110°  70°

14. Solve for the value of x and the measurements of the angles, given that each pair of angles are supplementary. C = (2x – 2)° & D = (x – 34)° 3 = (3x + 5)° & 4 = (5x + 5)° EFG = (x – 20)° & GFH = (x + 60)° J = ( 150 – x )° & K = (2x – 70)° LMN = (2x + 1)° & PQR = (3x – 1)°

15. Solve for the value of x and the measurements of the angles, given that each pair of angles are supplementary. C = (2x – 2)° & D = (x – 34)° 72 142 38 3 = (3x + 5)° & 4 = (5x + 5)° 15 100 80 EFG = (x – 20)° & GFH = (x + 60)° 80 60 120 J = ( 150 – x )° & K = (2x – 70)° 100 50 130 LMN = (2x + 1)° & PQR = (3x – 1)° 36 73 107

16. The Complement Theorem : Complements of congruent angles are congruent. Given: C and O are complementary P and M are complementary O  M Prove: C  P

17. The Complement Theorem : Complements of congruent angles are congruent. STATEMENT C and O are complementary P and M are complementary O  M mC + mO = 90 mP + mM = 90 mC + mO = mP + mM mO = mM mC = mP C  P REASON Given Definition of complementary angles Transitive Property of Equality Definition of congruent angles Subtraction Property of Equality Definition of congruent angles

18. Theorem : If two angles are complementary and adjacent, then they form a right angle.

19. The Supplement Theorem : Supplements of congruent angles are congruent.

20. Linear Pair A linear pair consists of two adjacent angles whose noncommon sides are opposite rays. Linear Pair Postulate : If two angles form a linear pair, then they are supplementary.

21. Vertical Angles Vertical angles are two nonadjacent angles formed by two intersecting lines.

22. Vertical Angle Theorem : Vertical angles are congruent.