Angles February 28, 2013

Review of Angles Right Angles = 90 Acute Angles = less than 90 Obtuse Angles = greater than 90 Straight Angles = 180

Complementary Angles What is it?What does it look like?What are examples? How to remember… The sum of 2 angles = 90° ° 35° 55° + 35° = 90° complementary Corner of a box

Supplementary Angles What is it?What does it look like?What are examples? How to remember… The sum of 2 angles = 180° ° 140° 40° + 140° = 180° supplementary Straight line

Vertical Angles What is it?What does it look like? Opposite angles form by the intersection of 2 lines Angle 1 and Angle 2 are vertical angles Angle 3 and Angle 4 are vertical angles

Straight Angles What is it?What does it look like? Angle that measures exactly 180° 1 Angle 1 = 180°

Find the measure that is complementary to the following angles 1.45° 2.88 ° 3.12 ° ° = 45 ° = 2 ° = 78 ° = 24.7 °

Find the measure that is supplementary to the following angles 1.124° ° 3.49 ° ° = 56 ° 180 – 149 = 2 ° = 78 ° 180 – = 24.7 °

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 x y Angle 1 and Angle 5 are corresponding angles Angle 3 and Angle 7 are corresponding angles Angle 2 and Angle 6 are corresponding angles Angle 4 and Angle 8 are corresponding angles

Alternate Interior Angles Angles are on opposite side of transversal Angles are between parallel lines x y Angle 3 and Angle 6 are alternate interior angles Angle 5 and Angle 4 are alternate interior angles

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 x y Angle 2 and Angle 7 are alternate exterior angles Angle 1 and Angle 8 are alternate exterior angles

Zig-Zap Method Line x is parallel to line y. Find the measure of each angle x y 4 120° 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°

Zig-Zap Method Line x is parallel to line y. Find the measure of each angle x y 4 120° 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°