Answer:
x = 20 , ∠ AEB = 91° , Y = 89
Explanation:
∠ AEB and ∠ CED are vertically opposite angles and are congruent (equal)
∠ AEB = ∠ CED ( substitute values )
5x - 9 = 3x + 31 ( subtract 3x from both sides )
2x - 9 = 31 ( add 9 to both sides )
2x = 40 ( divide both sides by 2 )
x = 20
----------------------------------
Then
∠ AEB = 5x - 9 = 5(20) - 9 = 100 - 9 = 91°
-------------------------------------
∠ AED and ∠ AEB are a linear pair and sum to 180°, that is
∠ AED + ∠ AEB = 180 ( substitute ∠ AEB = 9 and ∠ AED = y )
y + 91 = 180 ( subtract 91 from both sides )
y = 89