Question

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

Answer 1

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