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Complementary Angles Complementary angles are two angles whose measures have a sum of 90°.
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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°.
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Given that the two angles below are complementary, solve for the value of x and the angle measurements. mA 30 mB 2x + 10 30° 60° mA + mB 30 + 2x + 10 2x 2x x 90 90 90 – 30 – 10 50 25 = = = = =
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Given that the two angles below are complementary, solve for the value of x and the angle measurements. mC 2x + 20 mD 3x – 5 50° 40° mC + mD 2x + 20 + 3x – 5 2x + 3x 5x x 90 90 90 – 20 + 5 75 15 = = = = =
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Given that the two angles below are complementary, solve for the value of x and the angle measurements. mFEG 35 – x mGEH 45 + 2x 25° 65° mFEG + mGEH 35 – x + 45 + 2x – x + 2x x 90 90 90 – 35 – 45 10 = = = =
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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) °
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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
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Supplementary Angles Supplementary angles are two angles whose measures have a sum of 180°.
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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°.
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Given that the two angles below are supplementary, solve for the value of x and the angle measurements. mT 50 mV 3x + 40 50° 130° mT + mV 50 + 3x + 40 3x 3x X 180 180 180 – 50 – 40 90 30 = = = = =
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Given that the two angles below are supplementary, solve for the value of x and the angle measurements. mW 3x – 55 mX 155 – x 65° 115° mW + mX 3x – 55 + 155 – x 3x – x 2x x 180 180 180 + 55 – 155 80 40 = = = = =
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Given that the two angles below are supplementary, solve for the value of x and the angle measurements. mBYA 3x + 5 mAYZ 2x 110° 70° mBYA + mAYZ 3x + 5 + 2x 3x + 2x 5x x 180 180 180 – 5 175 35 = = = = =
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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)°
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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
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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
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The Complement Theorem: Complements of congruent angles are congruent. STATEMENT C and O are complementary P and M are complementary O M mC + mO = 90 mP + mM = 90 mC + mO = mP + mM mO = mM mC = mP C P REASON Given Definition of complementary angles Transitive Property of Equality Definition of congruent angles Subtraction Property of Equality Definition of congruent angles
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Theorem: If two angles are complementary and adjacent, then they form a right angle.
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The Supplement Theorem: Supplements of congruent angles are congruent.
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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.
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Vertical Angles Vertical angles are two nonadjacent angles formed by two intersecting lines.
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Vertical Angle Theorem: Vertical angles are congruent.
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