If ef bisects angle ceb, angle cef=7x+31 and angle feb=10x-3

Given : Angle < CEB is bisected by EF.

< CEF = 7x + 31.

< FEB = 10x-3.

We need to find the values of x and measure of < FEB, < CEF and < CEB.

Solution: Angle < CEB is bisected into two angles < FEB and < CEF.

Therefore, < FEB = < CEF.

Substituting the values of < FEB and < CEF, we get

10x - 3 = 7x + 31

Adding 3 on both sides, we get

10x - 3+3 = 7x + 31+3.

10x = 7x + 34

Subtracting 7x from both sides, we get

10x-7x = 7x-7x + 34.

3x = 34.

Dividing both sides by 3, we get

x = 11.33.

Plugging value of x=11.33 in < CEF = 7x + 31.

We get

< CEF = 7 (11.33) + 31 = 79.33+31 = 110.33.

< FEB = < CEF = 110.33 approximately

< CEB = < FEB + < CEF = 110.33 + 110.33 = 220.66 approximately