Question

Find x if EC is a bisectorAC = 3x+6 and CD = 2x + 14
a) 4
b) 8
c) 12
d) 16

Answer 1

To find x, we can use the angle bisector theorem and set up an equation based on the given information. Solving the equation, we find that x = 8.

Step-by-step explanation:

To find x, we can set up an equation using the fact that EC is a bisector. Since EC bisects angle ACB, we can use the angle bisector theorem which states that if a line bisects an angle in a triangle, it divides the opposite side into segments that are proportional to the other two sides. In this case, AC and CD are the two sides and EC is the bisector. So we have AC/CD = AE/ED.

Plugging in the given values, we get (3x+6)/(2x+14) = AE/ED.

Since EC is a bisector, AE = ED. So we can simplify the equation to (3x+6)/(2x+14) = 1. Cross multiplying, we have 3x+6 = 2x+14. Subtracting 2x from both sides, we get x = 8.