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2.2 Complementary and Supplementary Angles

2.2 Complementary and Supplementary Angles. Definition : Complementary Angles are two angles whose measures sum to 90. Each of the two angles is called the complement of the other. 1. 2. Adjacent Angles.

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2.2 Complementary and Supplementary Angles

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  1. 2.2 Complementary and Supplementary Angles

  2. Definition: Complementary Angles are two angles whose measures sum to 90. Each of the two angles is called the complement of the other.

  3. 1 2 Adjacent Angles • Definition: Two angles are called adjacent angles if they share a vertex and a common side. • Angles 1 and 2 are adjacent:

  4. Examples of Complementary Angles Adjacent Angles Non-Adjacent Angles

  5. Definition: Supplementary Angles are two angles whose measures sum to 180. Each of the two angles is called the supplement of the other.

  6. Examples of Supplementary Angles Adjacent Angles Non-Adjacent Angles

  7. Algebra & Angle Relationships You can find the complement of an angle that measures x° by subtracting its measure from 90°, or (90 – x)°. You can find the supplement of an angle that measures x° by subtracting its measure from 180°, or (180 – x)°.

  8. Example: Finding the Measures of Complements and Supplements Find the measure of each of the following. A. complement of F (90– x) 90 –59=31 B. supplement of G (180– x) 180– (7x+10)= 180 – 7x– 10 = (170– 7x)

  9. Another Example Find the measure of each of the following. a. complement of E (90– x)° 90°–(7x – 12)°=90°– 7x°+ 12° = (102 – 7x)° b. supplement of F (180– x) 180 – 116.5°=

  10. Verbal Description of Angle Relationships An angle is 10° more than 3 times the measure of its complement. Find the measure of the complement. Step 1 Let mA = x°. Then B, its complement measures (90 – x)°. Step 2 Write and solve an equation. x = 3(90 – x) + 10 Substitute x for mA and 90 – x for mB. x = 270 – 3x + 10 Distrib. Prop. x = 280 – 3x Combine like terms. 4x = 280 Divide both sides by 4. x = 70 Simplify. The measure of the complement, B, is (90 – 70) = 20.

  11. Verbal Description of Angle Relationships An angle’s measure is 12° more than half the measure of its supplement. Find the measure of the angle. Substitute x for mA and 180 - x for mB. x = 0.5(180 – x) + 12 x = 90 – 0.5x + 12 Distrib. Prop. x = 102 – 0.5x Combine like terms. 1.5x = 102 Divide both sides by 1.5. x = 68 Simplify. The measure of the angle is 68.

  12. Verbal Description of Angle Relationships • Two angles are complementary. • The angle measures are in the ratio 7:8. • Find the measure of each angle. • Solution: The angle measures can be represented by 7x and 8x. Then

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