Answer:
m∠EGF = 65° and m∠CGF = 115°
Step-by-step 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.
∴[tex]m\angle FEG = m\angle EGF[/tex]
Let the measure of ∠EGF be x.
∴ [tex]m\angle FEG = m\angle EGF = x[/tex]
Now by angle Sum property which states "The sum of all the angles of a triangle is 180°."
m∠EFG + m∠FEG + ∠EGF = 180
[tex]50\°+x+x=180\°\\50\°+2x=180\°\\2x= 180\°-50\°\\2x=130\°\\x=\frac{130}{2}= 65\°[/tex]
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°
