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

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


   

Question 155158: angle ABD = (3x +12), angle BDE = (7x-32). These angles are supplementary. Find the measures of both angles
Answer by Earlsdon(6294) About Me  (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.