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7-6 6 th grade math Angle Pairs

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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.

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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.

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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.

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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

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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°

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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 °

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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

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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 °

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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.

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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.

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