Angle Relationships

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Algebra and Geometry Using Angle Relationships

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What do we know about 3x complementary angles? x + 10 You could write this equation: (3x) + (x+ 10) = 90 Complementary Angles Their sum is 90º.

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Let’s solve for x: 3x + x + 10 = 90 4x + 10 = 90 -10 -10 4x = 80 4 4 x = 20 If x = 20, then 3x = 3(20) = 60º and x + 10 = 20 + 10 = 30º Check: 60 + 30 = 90 Yes, you need to find each angle and yes, you should double check that your answer makes sense.

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What do we know about supplementary angles? Supplementary angles add up to 180º Write an equation you could use to solve for x in this problem. 4x + x + 30 = 180 Supplementary Angles

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4x + x + 30 = 180 5x + 30 = 180 -30 -30 5x = 150 x = 30 Now find the measure for each angle: 4x = 4(30) = 120º x + 30 = 30 + 30 = 60º 120 + 60 = 180, so that works! 4x x + 30

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Vertical angles are congruent. How will that help us set up and equation? Congruent means the same so the angles are equal. 4x + 40 = 9x - 10 4x + 40 9x - 10 Vertical Angles

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4x + 40 = 9x – 10 -4x -4x___ 40 = 5x - 10 +10 + 10 50 = 5x 10 = x Find each angle. They should be the same. 4x + 40 4(10) + 40 40 + 40 80º 9x - 10 9(10) – 10 90 - 10 80º 80 80

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Alternate Interior Angles are congruent, too. 2x + 20 4x - 10 2x + 20 = 4x – 10 -2x -2x 20 = 2x – 10 +10 +10 30 = 2x 15 = x 2x + 20 4x – 10 2(15) + 20 4(15) – 10 30 + 20 60 – 10 50º 50º Alternate Angles

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Alternate Exterior Angles are also congruent. 6x 4x + 40 6x = 4x + 40 -4x -4x 2x = 40 x = 20 6x 4x + 40 6(20) 4(20) + 40 º 80 + 40 120º

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Corresponding Angles are congruent, too! 2x + 10 x + 35 2x + 10 = 1x + 35 -1x -1x 1x + 10 = 35 - 10 -10 x = 25 2x + 10 x + 35 2(25) + 10 25 + 35 50 + 10 60º 60º Corresponding Angles

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In summary….. Complementary angles add up to 90 (corner) Supplementary angles add up to 180 (straight) In all the others the angles are congruent, including Vertical angles X Alternate interior angles Z Corresponding angles F Alternate exterior angles