Question

Somebody please help me with this geometry work

Answer 1

m∠EGF = 65° and m∠CGF = 115°

Explanation:

Given;

∠EFG = 50°

EF = FG

Solution,

In ΔEFG m∠EFG = 50° and EF = FG.

Since triangle is an isosceles triangle hence their base angles are always equal.

∴
`m\angle FEG = m\angle EGF`

Let the measure of ∠EGF be x.

∴
`m\angle FEG = m\angle EGF = x`

Now by angle Sum property which states "The sum of all the angles of a triangle is 180°."

m∠EFG + m∠FEG + ∠EGF = 180

`50\°+x+x=180\°\\50\°+2x=180\°\\2x= 180\°-50\°\\2x=130\°\\x=(130)/(2)= 65\°`

Hence

m∠EGF = 65°

Also 'The sum of angles that are formed on a straight line is equal to 180°."

m∠EGF + m∠CGF = 180°

65° + m∠CGF = 180°

m∠CGF = 180° - 65° = 115°

Hence m∠EGF = 65° m∠CGF = 115°