I don't get this question.
EC bisects <BED, m<AEB =11x-12 and m<CED =4x+1. Find m<AEC
To find the measure of angle AEC, we can use the Angle Bisector Theorem. According to the theorem, the measure of angle AEC can be found by dividing the lengths of the two segments created by the bisector by their respective angles. In other words:
m<AEC = (m<AEB) / (m<CED)
Substituting the given values, we have:
m<AEC = (11x - 12) / (4x + 1)
This is the step-by-step approach to finding the measure of angle AEC using the Angle Bisector Theorem.
To find the measure of angle <AEC, we can start by using the angle bisector theorem. According to the theorem, the angle bisector divides the opposite side in the same ratio as the other two sides.
Let's call the measure of angle <AEC as y. Since EC bisects <BED, we can say that m<AEB + m<CED = m<AEC + m<CEB.
Substituting the given values, we have (11x-12) + (4x+1) = y + (y + m<CEB).
Now, simplify the equation:
15x - 11 = 2y + m<CEB.
Since the measure of <CEB is equal to the measure of <AEC (as they are opposite angles), we can write the equation as:
15x - 11 = 2y + y.
Combining the y terms, we have:
15x - 11 = 3y.
To find the value of y, we need to know the value of x, which is not given in the question. If a value for x is provided, we can substitute it into the equation 15x - 11 = 3y and solve for y.