Question

Lines AB and CD intersect at E

D

A

E

50°

B

What is the measure of angle AED? Explain how you know.

Answer 1

Explanation:

Here is the complete question.

Line AB and CD intersect at E. If angle AEC = 4 x−40 and angle BED = x + 50 , what is the number of degrees in AEC?

If lines AB and CD intersect at E , then <AEC = <BED (oppositely directed angles)

Given

<AEC = 4 x−40

<BED = x + 50

If <AEC = <BED, then;

4x-40 = x+50

4x-x = 50+40

3x = 90

x = 90/3

x = 30°

Also note that <AED + <AEC = 180

<AEC = 4x-40

<AEC = 4(30)-40

<AEC = 120-40

<AEC = 80

<AED +80 = 180

<AED = 180-80

<AED = 100

Hence the measure of angle AED is 100°