Ray EC bisects ∠BED, m ∠AEB=11x-12 and m ∠CEB=4x+1. Find m ∠AEC.
Since Ray EC bisects ∠BED, this means that ∠AEC = ∠CEB.
Since ∠AEB = ∠CEB, we can set the two expressions equal to each other:
11x - 12 = 4x + 1
Subtract 4x from both sides:
7x - 12 = 1
Add 12 to both sides:
7x = 13
Divide both sides by 7:
x = 13/7
Now that we have the value of x, we can find ∠AEC by substituting it back into the given expression:
m ∠AEC = 4x + 1
= 4(13/7) + 1
= 52/7 + 1
= 52/7 + 7/7
= 59/7
Therefore, m ∠AEC = 59/7.