First lets find the value of x. We can do this by making m∠AEB and m∠DEC equal to each other in an equation because they are vertical angles (vertical angles are equal to each other).
Your equation should look like this: m∠AEB = m∠DEC
Plug in the values of m∠AEB and m∠DEC into the equation. Now your equation should look like this:
(3x + 21) = (2x + 26)
Subtract 2x from both sides.
x + 21 = 26
Subtract 21 from both sides.
x = 5
Now plug 5 for x in either ∠AEB or ∠DEC; I will plug it into ∠AEB.
m∠AEB = 3(5) + 21
15 + 21 = 36
m∠AEB = 36°, now since ∠AEB and ∠AED are forming a straight line, this means they are supplementary so they must add up to 180 degrees.
Make m∠AEB and m∠AED add up to 180 in an equation and solve for m∠AED.
36 + m∠AED = 180
Subtract 36 from both sides.
m∠AED = 144°
