1. 7-6 6 th grade math Angle Pairs

2. Objective To find the measure of an unknown angle from its relationship to other angles Why? To know how to ‘read’ angle pairs will help you get a good foundation for geometry, later in high school math.

3. California State Standards MG 2.2 : Use the properties of complementary and supplementary angles … to solve problems involving an unknown angle. MG 2.1: Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these forms. AF 1.1 : Write and solve one-step linear equations in one variable. AF 3.2: Express in symbolic form simple relationships arising from geometry.

4. Vocabulary Vertical angles – Two angles formed by intersecting lines and having no sides in common. They have the same angle ∠ m. ̮͡ Supplementary angles – Two angles whose sum of their measures equals 180 ° Complementary angles – Two angles whose sum of their measures equals 90 ° Adjacent angles – Two angles that have a common vertex and a common side but do not overlap.

5. Vocabulary Intersecting angles or lines – Two lines or angles that have exactly one point in common Perpendicular lines – Two lines that intersect and form a 90 ° angle ┐ Parallel lines – Two lines that will never intersect each other

6. How to Find Measures of Angles w/o a Protractor 1) Observe and/or trace the angles needed to be identified: adjacent?, supplementary?, complementary?, vertical? 2) If vertical, the angles are the same. If adjacent, are angles supplementary or complementary? If supplementary, subtract from 180 °. If complementary, subtract from 90 °. 3) Check your work. F 147 ° H E G J ∠ GEJ and ∠ FEH are vertical angles ∠ GEJ = 147 °, so ∠ FEH = 147 ° If ∠ GEH = 180°, ∠ GEJ = 147 °, so ∠ HEJ = 180 - 147 = 33. ∠ HEJ = 33° Then ∠ HEJ = 33°, so ∠ GEF = 33°

7. How to Find Measures of Angles w/o a Protractor C 50 ° A O D ∠AOC and ∠COD are adjacent, supplementary angles, and m∠COD = 50 °. Find ∠AOC. 180 – 50 = 130 ∠AOC = 130 ° N M 25 ° L K ∠KLM and ∠MLN are adjacent, complementary angles and m∠MLN = 25 °. Find ∠KLM. 90 – 25 = 65 ∠KLM = 65 °

8. Try It! Find the ∠ m. 1) a 35° 2) 79° b 3) 110° c 4) d 50° 130° 1)55, complementary 2)79, vertical 3)70, supplementary 4)80, supplementary

9. 5) Draw: m ∠ of 120 ° with an adjacent supplementary angle, name this angle. 6) Draw: m ∠ of 45 ° with an adjacent, name this angle. 7) Two angles that are congruent and supplementary. What are their m ∠ ? 5) 60 ° 120° 6) 45 ° 45 ° 7)90 ° and 90 °

10. Objective Review To find the measure of an unknown angle from its relationship to other angles Why? You now know how to ‘read’ angle pairs will help you get a good foundation for geometry, later in high school math. Knowing the relationships of certain pairs of angles can help you find the measure of an unknown angle.

11. Independent Practice Complete problems 8- 19 Copy original problem first. Show all work! If time, complete Mixed Review: 20-22 If still more time, work on Accelerated Math.