# SOLUTION: angle ABD = (3x +12), angle BDE = (7x-32). These angles are supplementary. Find the measures of both angles

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 Geometry: Angles, complementary, supplementary angles Solvers Lessons Answers archive Quiz In Depth

 Question 155158: angle ABD = (3x +12), angle BDE = (7x-32). These angles are supplementary. Find the measures of both angles Answer by Earlsdon(6287)   (Show Source): You can put this solution on YOUR website!If the angles are supplementary, then: ABD = 180-BDE or... (3x+12) = 180-(7x-32) Simplify and solve for x. 3x+12 = 180-7x+32 3x+12 = 212-7x Add 7x to both sides. 10x+12 = 212 Subtract 12 from both sides. 10x = 200 Divide both sides by 10. x = 20 degrees. Angle ABD = 3x+12 = 3(20)+12 = 60+12 = 72 degrees. Angle BDE = 180-ABD = 180-72 = 108 degrees. Check: ABD+BDE = 72+108 = 180 The angles are supplementary.