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Teacher: Mr. Joseph Introduction to Angles Name:__________________________ Period: ________ Date: ____________ Solve: 1) 2) What does supplementary mean? SILYM is a regular pentagon. What is m SEI? 3) C and G are congruent. m C = 30°. What is m G? 4) A and W are complementary. m A = 30°. What is m W? 5) __ → FY is bisected by LO. 6) __ CT is bisected by AN. If FL = x + 31 and LY = 5x + 19, what is FY? If CA = 5x + 2 and CT = 4x + 52, what is AT? Solve for x: 7) (2x -3)° (5x -8)° 8) (12x -7)° (2x + 3)° 9) (13x -12)° 10) (2x + 17)° (5x + 16)° (6x + 5)° Solve: 11) In JTQ, m Q = (-13x + 85)°, m T = 12) (-2x + 60)°, and m J = (2x + 100)°. What is x? 13) 14) m P = (x + 9)°, m N = (x + 15)°, and m SIP = (-4x + 60)°. Solve for x. m AWR = (x + 10)°, m PRW = (x + 9)°, and m PAW = (11x -107)°. Solve for x. 15) In NYW, m N = (-20x + 410)°, m Y = (-18x + 324)°, and m W = (4x + 24)°. What is m N? 16) m P = 71°, m N = 4°. Find m SIP. m WFR = 113°, m PRF = 30°. Find m RAW. EasyWorksheet Step By Step Answers User Name: J. Joseph Form #46261171149 Practice Problems 1) SILYM is a regular pentagon. What is m SEI? All of the angles around the center (point E) are the same, and they sum to 360°, so we take 360 and divide by 5 to get 72° 2) What does supplementary mean? We use supplementary to mean that two angles sum to 180° 3) C and G are congruent. m C = 30°. What is m G? Congruent means that the angles are the same. So we get 30° 4) A and W are complementary. m A = 30°. What is m W? Complementary means that the angles sum to 90°. So we get 90 - 30 = 60° 5) __ → FY is bisected by LO. If FL = x + 31 and LY = 5x + 19, what is FY? Since FY is bisected, the picture actually looks like: . So LY = FL. And FY is twice that value. So x + 31 = 5x + 19 -4x + 31 = 19 -4x = -12 x=3 But we need to make sure we answer the question! Plug back in x to get: FY= 2(FL) = 2((3) + 31) = 68 6) __ CT is bisected by AN. If CA = 5x + 2 and CT = 4x + 52, what is AT? Since CT is bisected, the picture actually looks like: . So AT = CA. And CT is twice that value. So 2(5x + 2) = 4x + 52 10x + 4 = 4x + 52 6x + 4 = 52 6x = 48 x=8 But we need to make sure we answer the question! Plug back in x to get: AT= CA = 5(8) + 2 = 42 7) (2x -3)° (5x -8)° Since these are vertical angles, we set (2x -3)° equal to (5x -8)°: (2x -3)° = (5x -8)° Move all your terms so that your variable is on one side, and your constants are on the other side of the equation: 2x + -5x = -8 + 3 Next combine your like terms to get: -3x = -5 Finally, divide both sides of the equation by -3: So x = 5/3 8) (12x -7)° (2x + 3)° Since these are vertical angles, we set (12x -7)° equal to (2x + 3)°: (12x -7)° = (2x + 3)° Move all your terms so that your variable is on one side, and your constants are on the other side of the equation: 12x + -2x = 3 + 7 Next combine your like terms to get: 10x = 10 Finally, divide both sides of the equation by 10: So x = 1 9) (13x -12)° (5x + 16)° Since these create a linear pair, we know that (13x -12)° and (5x + 16)° are supplementary: (13x -12)° + (5x + 16)° = 180° 18x + 4 = 180 Move all your terms so that your variable is on one side, and your constants are on the other side of the equation: 18x = 180 + -4 Next combine your like terms to get: 18x = 176 Finally, divide both sides of the equation by 18: So x = 88/9 10) (2x + 17)° (6x + 5)° Since these create a linear pair, we know that (2x + 17)° and (6x + 5)° are supplementary: (2x + 17)° + (6x + 5)° = 180° 8x + 22 = 180 Move all your terms so that your variable is on one side, and your constants are on the other side of the equation: 8x = 180 + -22 Next combine your like terms to get: 8x = 158 Finally, divide both sides of the equation by 8: So x = 79/4 11) In JTQ, m Q = (-13x + 85)°, m T = (-2x + 60)°, and m J = (2x + 100)°. What is x? In a triangle, the angles sum to 180° so we set up the following equation: 180° = (-13x + 85)° + (-2x + 60)° + (2x + 100)° 180 = -13x + 85 + -2x + 60 + 2x + 100 180 = -13x + 245 -65 = -13x 5=x So, x = 5 12) In NYW, m N = (-20x + 410)°, m Y = (-18x + 324)°, and m W = (4x + 24)°. What is m N? In a triangle, the angles sum to 180° so we set up the following equation: 180° = (-20x + 410)° + (-18x + 324)° + (4x + 24)° 180 = -20x + 410 + -18x + 324 + 4x + 24 180 = -34x + 758 -578 = -34x 17 = x So, x = 17 Filling this back in for N, we get 70° 13) m AWR = (x + 10)°, m PRW = (x + 9)°, and m PAW = (11x -107)°. Solve for x. In a triangle, the two opposite interior angles sum to the exterior angle. This means we can set up an equation: x + 10 + x + 9 = 11x -107 2x + 19 = 11x -107 Moving our constants to the right and any variables to the left, we get: -9x = -126 So we end up with x = 14 14) m P = (x + 9)°, m N = (x + 15)°, and m SIP = (-4x + 60)°. Solve for x. In a triangle, the two opposite interior angles sum to the exterior angle. This means we can set up an equation: x + 9 + x + 15 = -4x + 60 2x + 24 = -4x + 60 Moving our constants to the right and any variables to the left, we get: 6x = 36 So we end up with x = 6 15) m WFR = 113°, m PRF = 30°. Find m RAW. Using the Triangle Sum Theorem, we get: 180° = m WFR + m PRF + m FAR. 180° = 113° + 30° + m FAR. So m FAR = 37°. RAW is a linear pair with FAR, so by the Linear Pair Postulate, these are supplementary angles: 180° = m RAW + m FAR 180° = m RAW + 37° So m RAW = 143° 16) m P = 71°, m N = 4°. Find m SIP. We can use the Triangle Sum Theorem to conclude: m PIN = 180° - 71° - 4° m PIN = 105° But we are looking for m SIP! We can use the fact that PIN and SIP are a linear pair, so they are supplementary. m SIP = 180° - 105° = 75° All rights reserved. This page is copyright 1998 Triple Threat Inc. Any violators will be prosecuted through full extent of the law.