Question

Angle EBC=3r+10
Angle ABE=2r-20
Find angle EBF

Answer 1

The angles EBC & ABE form a linear pair.

So, ∠EBC + ∠ABE= 180

3r+10+2r-20 = 180

5r-10=180

5r=180+10

5r=190

r=190/5

r=38

Substitude

Since, ∠EBF = ∠ABE

∠EBF = 2r-20

∠EBF = 2(38)-20

∠EBF=76-20

∠EBF=56 (Answer)

Answer 2

The measure of angle m<EBF is 56degrees given that angle EBC=3r+10 and angle ABE=2r-20

The point where two lines meet is known as an angle.

Find the diagram attached

The sum of angle EBC and ABE is supplementary, hence:

m<EBC + m<ABE = 180degree

3r+10+2r-20 = 180

3r+2r - 10 = 180

5r = 180 + 10

5r = 190

r = 190/5

r = 38degrees

Next is to get the angle m<EBF.

From the given diagram, the m<ABE = m<EBF

m<EBF = 2r - 20

m<EBF = 2(38)-20

m<EBF = 76 - 20

m<EBF = 56degrees

Hence the measure of angle m<EBF is 56degrees