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.
Since line EC bisects angle BED, it means that angle AEC and angle CED are congruent.
Let's represent the measure of angle AEC as y.
Thus, the measure of angle CED is also y.
According to the information given, the measure of angle AEB is 11x - 12.
Therefore, we can set up the equation: 11x - 12 = y.
Similarly, the measure of angle CED is 4x + 1.
So, we can set up another equation: 4x + 1 = y.
Since angles AEC and CED are congruent, we can set these two equations equal to each other:
11x - 12 = 4x + 1.
By simplifying this equation, we get:
11x - 4x = 1 + 12.
7x = 13.
Dividing both sides by 7, we find:
x = 13/7.
To find the measure of angle AEC (y), we need to substitute this value of x into one of the equations, let's use the equation 11x - 12 = y:
11(13/7) - 12 = y.
143/7 - 84/7 = y.
59/7 = y.
Thus, the measure of angle AEC is 59/7.