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Transcript
Seventh Grade Geometry Unit 4 MGSE7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. Essential Question How can I use the special angle relationships – supplementary, complementary, vertical, and adjacent – to write and solve equations for multi-step problems? Types of Angles Right, Acute, or Obtuse Two lines that will never intersect Two lines that intersect and form four right angles Opposite angles that are formed by intersecting lines. These angles are equal to each other. Two angles that share a common ray. Two angles that add up to 90° Two angles that add up to 180° Angle Style Complementary Angles – angles that add up to 90º Supplementary Angles – angles that add up to 180º Complementary 20 + x = 90 -20 - 20 x = 70 Supplementary 115 + x = 180 -115 - 115 x = 65 How can I remember which angle is which… complementary or supplementary? Linear Pair Two adjacent angles that form a line. They are supplementary. (angle sum = 180) t 1+2=180 2+4=180 4+3=180 3+1=180 1 2 3 4 Supplementary Angles/ Linear Pair Find the measures of the missing angles t 108? 72 72 108 ? 72 + x = 180 -72 -72 x = 108 Who uses this stuff? Congruent Angles – Angles with equal measurement A ≅ B means that A is congruent to B. Adjacent Angles - angles that share a common vertex and ray…angles that are back to back. *Vertex – the “corner” of the angle *Ray – a line that has an endpoint on one end and goes on forever in the other direction. Vertical Angles Two angles that are opposite angles at intersecting lines. Vertical angles are congruent angles. t 1 2 3 4 1 4 2 3 Vertical Angles Hint: V and A are facing opposite directions and are the same shape. Vertical Angles are facing opposite each other and are the same measurement. Vertical Angles Find the measures of the missing angles t 125 ? 125 55 ? 55 Name the angles and write an equation to find the angle measurements. 3(15) 45° complementary 45 + 3x = 90 -45 -45 3x = 45 ÷3 ÷3 x = 15 supplementary 3x + 25 + 2x = 180 5x + 25 = 180 2(31) 62° -25 -25 5x = 155 3(31)+25 ÷5 ÷5 118° x = 31 55° 55-20 35° 4(33.5)+5 139° complementary x + x – 20 = 90 2x – 20 = 90 +20 +20 2x = 110 ÷2 ÷2 x = 55 supplementary 4x + 5 + 41 = 180 4x + 46 = 180 -46 -46 4x = 134 ÷4 ÷4 x = 33.5 Name the angles and write an equation to find the angle measurements. 4•25-25 75° 7(20) 140° vertical 4x - 25 = 75 +25 +25 4x = 100 ÷4 ÷4 x = 25 supplementary 7x + x + 20 = 180 8x + 20 = 180 -20 -20 8x = 160 20+20 40° ÷8 ÷8 x = 20 complementary 4x + 2x = 90 6x = 90 ÷6 ÷6 x = 15 4(15) 60° 2(15) 30° complementary 69 + 2x -1 = 90 68 + 2x = 90 -68 -68 2x = 22 ÷2 ÷2 x = 11 2•11-1 21° Closing add up to 90° • Complementary Angles ______________ add up to 180° • Supplementary Angles ______________ are congruent • Vertical Angles ____________________