Geometry 8 th Grade Algebraic Angles Essential Questions

Geometry 8 th Grade Algebraic Angles

Essential Questions How can I use the special angle relationships – supplementary, complementary, vertical, and adjacent – to write and solve equations for multi-step problems?

How can I remember which angle is which? complementary or supplementary?

Review Complementary Angles–angles that add up to 90º

Review Supplementary Angles – angles that add up to 180º

Complementary 20 + x = 90 -20 - 20 x = 70 Supplementary 115 + x = 180 -115 - 115 x = 65

Linear Pair Two adjacent angles that form a line. They are supplementary. (angle sum = 180 ) 1+ 2=180 2+ 4=180 4+ 3=180 3+ 1=180 t 1 2 3 4

Supplementary Angles/ Linear Pair Find the measures of the missing angles t 108? 72 108 ? 180 - 72

Who uses this stuff?

Congruent Angles – Angles with equal measurement A ≅ B denotes 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

Review: Determine if the given angles are complementary, supplementary, vertical, or adjacent. 1) 2) 3) 4) g and f complementary b, c, and d supplementary f and e adjacent a and d vertical

30° 55° 125° 55°

Solve for x and find the algebraic angle. 5 x + 10 = 110 -10 5 x = 100 ÷ 5 x = 20

Name the types of angles and solve for the algebraic angle. . . also known as a linear pair.

Write an equation and solve for both angles. x + 3 x + 10 = 90 x 3 x + 10 3(20) + 10 70 4 x + 10 = 90 - 10 -10 4 x = 80 4 4 x = 20

Write an equation and solve for both angles. x 2 x - 30 x + (2 x - 30) = 180 3 x - 30 = 180 +30 3 x = 210 x = 70 2(70) – 30 = 110 70

Write an equation to solve for x. x + 38 = 90 x = 52

Write an equation to solve for x and find the algebraic angle. 110º 5 x + 110 = 180 x = 14 5(14) = 70º

Write an equation to solve for x and then find the two angle measurements. 4 xº 4 x + x = 180 5 x = 180 x = 36º 4(36) = 144º xº

Solve for x. 83º (2 x + 1)º 2 x + 1 = 83 x = 41

Solve for x and then find the angle measurements. 2 xº 2 x = 5 x – 108 = 3 x 36 = x (5 x -108)º 2(36) = 72º 5(36) – 108 = 72º

Write equations to find the missing angles. 2 xº 12º 7 x + 6 = 90 x = 12 Solve for x. ______ Solve for angle 7(12) + 6 = 90° F. ______ 2 x + 12 = 90 Solve for x _______ x = 39 78° Solve for the missing angle ____

Exit Slip • Explain how you find angle measures using Algebra.

Triangles

180 Rule for Triangles - the sum of the interior angles of any triangle is always 180. b 80 40 a 40 x c + 80 + x = 180 120 + x = 180 x = 60

Find each angle below. 2 y - 10 y + 14 = 63 2 y - 10 = 88 y - 20 = 29 y+14 y - 20 180 (y + 14) + (2 y - 10) + (y - 20) = 180 4 y - 16 = 180 +16 4 y = 196 y = 49

Find the missing angle. x 92° 40 48° 132

Find the missing angle. 119 61° 63°x 56° 124

Write and solve equations to find the angles below. 1. 5 + x + 117 = 180° 2. x = 58 2 x + 8 + 3 x + 2 = 90° 5 + 58 = 63° x = 16 2(16) + 8 = 40° 3(16) + 2 = 50° 3. 4. 145 + z = 180° z = 35° 110 + x = 180° x = 70° 35 + 70 + y = 180° y = 75° x° z° 3 x + 20 + 2 x + 10 = 90° x = 10 3(10) = 30° (10) + 20 = 30° 2(10) + 10 = 30°

Find e. e = 25° because vertical angles are equal. Sometimes it is easier than you first think to solve for the missing angle.

41° Solve for n. n° 105° 113° 67° 101° 79° 34°

One angle in a pair of vertical angles is (4 t + 16)º and the other angle is (5 t – 21)º. congruent 1) Vertical angles are ______. 2) Write the equation that you will use to find the angle 5 t – 21 = 4 t + 16 measurements. ______ 37º 3) t = _____ 164º 4) The two angle measurements are _____ and 164º _______.

1. Find the measures of the angles labeled A, B, and C. 2. Find the measures of the angles labeled a, b, c, and d. 72° 60° 65° 72° 61° 47° 30° 55°

In a linear pair of angles, one angle is three times larger than the other angle. supplementary 1) Linear pair angles are ________. 2) The equation I will use to solve for the angle x + 3 x = 180 measurements is _______. 45º 3) X = ______ 45º 4) The angle measurements are ______ and 135º _______.

Closing Write an equation to solve for x and then find the missing angle measurement. x = 21 5(21) = 105° x = 10 5(10) + 2 = 52°