ray EC bisects angle BED, The measure of angle AEB equals 11x minus 12.and The measure of angle CED equals 4x plus 1.. Find measure of angle AEC.Horizontal line AED shown with line segments EB and EC extending upward.
(2 points)
Since line EC bisects angle BED, we know that angle AEC and angle CED are congruent.
Let's denote the measure of angle AEC as y.
Therefore, measure of angle AEB = 2y (since line EC bisects angle BED)
According to the given information, measure of angle AEB = 11x - 12
So we can write the equation: 2y = 11x - 12
And measure of angle CED = 4x + 1
Since angle AEC and angle CED are congruent, we can write another equation: y = 4x + 1
Now we have a system of two equations:
2y = 11x - 12
y = 4x + 1
To solve this system, we can substitute the value of y from the second equation into the first equation:
2(4x + 1) = 11x - 12
8x + 2 = 11x - 12
8x - 11x = -12 - 2
-3x = -14
x = (-14)/(-3)
x = 14/3
Substitute the value of x back into the second equation to find y:
y = 4(14/3) + 1
y = 56/3 + 1
y = 56/3 + 3/3
y = 59/3
So the measure of angle AEC is 59/3 degrees.