Vertices D and F of DEF lie on CG, the measure of ∠CDE is 148°

In the figure below, vertices D and F of DEF lie on CG, the measure of ∠CDE is 148°, and the measure of ∠EFG is 140°. What is the measure of ∠DEF ?

1. 072°
2. 098°
3. 100°
4. 108°
5. 116°

Answer

The correct answer is D.

Using the properties of supplementary angles,

∠EDF = 180° - 148° = 32°

∠EFD = 180° - 140° = 40°

By the 180° rule for triangles,

∠DEF = 180° - 32° - 40° = 108°