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# AB and CD intersect at E. If measure of angleAEC=5x-20 and measure of angleBED=x+52, find measure of angleCEB?

I keep getting 116 but it's supposed to be 110 according to my book, can someone please give step by step instructions?

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- flavyLv 410 years agoFavorite Answer
angle AEC=angle BED from theorem in Geometry

therefore;

5x-20=x+52

5x-x=52+20

4x=72

x=18

therefore, angle AEC=BED=5(18)-20= 18+52= 70

THE SUM OF ALL THE ANGLE =360

360= angles, ( AEC+BED+CEB+AED)

CEB=AED & AEC=BED

360= 2(70) +2(CEB)

CEB=[ 360-2(70)]/2 = 110

- Anonymous10 years ago
5x-20=x+52

4x=72

x=18

measure of angle CEB=180-5*18-20=110

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