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.
To find the measure of angle AEC, we need to know the relationship between angle AEB and angle CED, and then use that relationship to find the measure of angle AEC.
Since ray EC bisects angle BED, we know that angle AEC is equal to angle CED. Therefore, to find the measure of angle AEC, we need to find the measure of angle CED.
Given that the measure of angle CED is 4x + 1, we can substitute this expression into angle AEB, and set them equal to each other:
11x - 12 = 4x + 1
Subtract 4x from both sides of the equation to isolate the x term:
11x - 4x - 12 = 4x - 4x + 1
7x - 12 = 1
Add 12 to both sides of the equation:
7x - 12 + 12 = 1 + 12
7x = 13
Divide both sides of the equation by 7 to solve for x:
7x/7 = 13/7
x = 13/7
Now that we have the value of x, we can substitute it back into the expression for angle CED to find its measure:
CED = 4x + 1
CED = 4(13/7) + 1
CED = 52/7 + 1
CED = 52/7 + 7/7
CED = 59/7
Therefore, the measure of angle CED is 59/7.
Since angle AEC is equal to angle CED, the measure of angle AEC is also 59/7.
To find the measure of angle AEC, we can use the fact that ray EC bisects angle BED. This means that the measure of angle AEC is equal to half the measure of the entire angle AEB.
Let's denote the measure of angle AEC as y.
According to the given information:
The measure of angle AEB equals 11x - 12.
The measure of angle CED equals 4x + 1.
Since ray EC bisects angle BED, angle AEB and angle CED are congruent. So we can set up the equation:
11x - 12 = 4x + 1
Now, let's solve this equation for x:
11x - 4x = 1 + 12
7x = 13
x = 13/7
Now that we have the value of x, we can substitute it back into the equation for angle AEC:
y = 11x - 12
y = 11(13/7) - 12
y = 143/7 - 12
y = (143 - 84)/7
y = 59/7
Therefore, the measure of angle AEC is 59/7 or approximately 8.43 degrees.