Answer:
m∠E = 77°
Explanation:
∠EFM and ∠EFD are supplementary angles, meaning their sum is 180°.
If m∠EFM = 117°, then m∠EFD = 180 - 117 = 63°.
We also know that the angle sum for any triangle is 180°. So...
m∠EFD + m∠D + m∠E = 180°
63° + 40° + m∠E = 180°
m∠E = 77°
The other way to do this question is to see that 117° is an exterior angle of the triangle and that the other two angles (∠D and ∠E) should sum to 117°.
m∠D + m∠E = 117°
40° + m∠E = 117°
m∠E = 77°