Question

Applying Angle Relationships of Isosceles Triangles

Answer 1

(180(total angle measure of triangle)-50(EFG))/2(the other two angles have the same measure)=65


The angle CGE=180=CGF+EGF
180-65=CGF
115=CGF

Answer 2

we know that

An isosceles triangle has two equals sides and two equals angles

so

EF=GF

m∠EGF=m∠GEF

The sum of the internal angles of a triangle must be $180$ degrees

m∠EGF+m∠GEF+m∠EFG=$180\°$

we have

m∠EFG=$50\°$

2m∠EGF+$50\°=180\°$

2m∠EGF=$180\°-50\°$

2m∠EGF=$130\°$

m∠EGF=$65\°$

therefore

the answer Part a) is

the measure of angle EGF is $65\°$

Part b) What is the measure of m∠CGF?

we know that

m∠CGF+m∠EGF=$180\°$ ---------> by supplementary angles

substitute values

m∠CGF+$65\°=180\°$

m∠CGF=$180\°-65\°$

m∠CGF=$115\°$

therefore

the answer Part b) is

the measure of angle CGF is $115\°$