1. Angles February 28, 2013

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

3. 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

4. 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

5. 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

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

7. 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 °

8. 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 °

9. 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

10. 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

11. 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

12. 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°

13. 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°