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
