Answer:
Answer is ∠AEC = 139 degrees.
Step-by-step explanation:
You always want to set these questions up in terms of what you know, and how you can use what you know to find the answer. There are a few things we know right off the bat:
1. The value of ∠AEB and ∠CED.
2. Since AED is a straight line, ∠AEC + ∠CED = ∠AED = 180
3. Since EC bisects ∠BED, ∠BEC = ∠CED
We want to find ∠AEC. If we can construct an equation to solve for that angle using the known things above, we can plug n play the variables at the end.
The most direct way to do that is subtracting:
∠AEC = ∠AED - ∠CED
We know the values of ∠AED and ∠CED from the question, but not ∠AEC. We need to express ∠AEC in terms of things we already know. You'll notice that ∠AEC = ∠AEB + ∠BEC. We know the value of both those angles, so we can rewrite the equation, then substitute, then solve:
∠AEB + ∠BEC = ∠AED - ∠CED
11x - 12 + 4x + 1 = 180 - 4x - 1
15x - 11 = 179 - 4x
19x = 190
x = 10
Now that we know the value of x, we can solve for the value of ∠AEC using (2) above:
∠AEC + ∠CED = 180
∠AEC = 180 - ∠CED
∠AEC = 180 - 4x - 1
∠AEC = 180 - 4(10) - 1
∠AEC = 180 - 40 - 1
∠AEC = 139