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Angles February 28, 2013
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Review of Angles Right Angles = 90 Acute Angles = less than 90 Obtuse Angles = greater than 90 Straight Angles = 180
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Complementary Angles What is it?What does it look like?What are examples? How to remember… The sum of 2 angles = 90° 1 2 55° 35° 55° + 35° = 90° complementary Corner of a box
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Supplementary Angles What is it?What does it look like?What are examples? How to remember… The sum of 2 angles = 180° 1 2 40° 140° 40° + 140° = 180° supplementary Straight line
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Vertical Angles What is it?What does it look like? Opposite angles form by the intersection of 2 lines 12 3 4 Angle 1 and Angle 2 are vertical angles Angle 3 and Angle 4 are vertical angles
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Straight Angles What is it?What does it look like? Angle that measures exactly 180° 1 Angle 1 = 180°
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Find the measure that is complementary to the following angles 1.45° 2.88 ° 3.12 ° 4.65.3 ° 90-45 = 45 ° 90-88 = 2 ° 90-12 = 78 ° 90-65.3 = 24.7 °
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Find the measure that is supplementary to the following angles 1.124° 2.149 ° 3.49 ° 4.138.4 ° 180-124 = 56 ° 180 – 149 = 2 ° 180 - 49 = 78 ° 180 – 138.4 = 24.7 °
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Corresponding Angles Angles are in the same position Formed by a transversal cutting 2 or more lines If transversal goes through parallel lines, then corresponding angles are congruent 1 3 5 7 x y Angle 1 and Angle 5 are corresponding angles 2 4 8 6 Angle 3 and Angle 7 are corresponding angles Angle 2 and Angle 6 are corresponding angles Angle 4 and Angle 8 are corresponding angles
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Alternate Interior Angles Angles are on opposite side of transversal Angles are between parallel lines 1 3 5 7 x y Angle 3 and Angle 6 are alternate interior angles 2 4 8 6 Angle 5 and Angle 4 are alternate interior angles
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Alternate Exterior Angles Angles are opposite side of transversal Formed outside of parallel lines If transversal goes through parallel lines, then alternate exterior angles are congruent 1 3 5 7 x y Angle 2 and Angle 7 are alternate exterior angles 2 4 8 6 Angle 1 and Angle 8 are alternate exterior angles
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Zig-Zap Method Line x is parallel to line y. Find the measure of each angle. 1 3 5 7 x y 4 120° 6 2 8 Since Angles 7 and 8 are supplementary, then Angle 7 must equal 60° 60° Since Angles 8 and 1 are alternate exterior angles, then Angle 1 must equal 120° Since Angles 8 and 5 are vertical angles, then Angle 5 must equal 120° Since Angles 7 and 6 are vertical angles, then Angle 6 must equal 60° 120° 60°
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Zig-Zap Method Line x is parallel to line y. Find the measure of each angle. 1 3 5 7 x y 4 120° 6 2 8 Since Angles 1 and 2 are supplementary, then Angle 2 must equal 60° 60° Since Angles 2 and 3 are vertical angles, then Angle 3 must equal 60° Since Angles 1 and 4 are vertical angles, then Angle 4 must equal 120° Now note the zig zag pattern 120° 60° 120°
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