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# Angle Pairs

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• 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
 30°
 60°
mA + mB
30 + 2x + 10
2x
2x
x
90
90
90 – 30 – 10
50
25
=
=
=
=
=
• 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
 50°
 40°
mC + mD
2x + 20 + 3x – 5
2x + 3x
5x
x
90
90
90 – 20 + 5
75
15
=
=
=
=
=
• 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
 25°
 65°
mFEG + mGEH
35 – x + 45 + 2x
– x + 2x
x
90
90
90 – 35 – 45
10
=
=
=
=
• 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
 50°
 130°
mT + mV
50 + 3x + 40
3x
3x
X
180
180
180 – 50 – 40
90
30
=
=
=
=
=
• 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
 65°
 115°
mW + mX
3x – 55 + 155 – x
3x – x
2x
x
180
180
180 + 55 – 155
80
40
=
=
=
=
=
• 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
 110°
 70°
mBYA + mAYZ
3x + 5 + 2x
3x + 2x
5x
x
180
180
180 – 5
175
35
=
=
=
=
=
• 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.