Question

For questions 4-7, find the measures of the angles in the picture below.

(Questions shown in image)​

Answer 1

Measures of each angle are as follows:

4. ∠BXC = 20°

5. ∠FXE = 85°

6. ∠GXD = 75°

7. ∠BXF = 75°

Explanation:

#4
∠BXC is opposite ∠EXD and so it is the same as ∠EXD = 20°

#5
∠FXE is opposite ∠CXG and so it is the same as ∠CXG = 85°

#6
Angles ∠CXG, ∠GXD and ∠EXD line on a straight line so the sum of these angles must be 180°
∴ m∠CXG + m∠GXD + m∠EXD = 180°

Substituting known values for ∠CXG and ∠EXD we get
85 + ∠GXD + 20 = 180°
105 + m∠GXD = 180°
m∠GXD = 180-105 = 75°

#7
∠BXF is opposite ∠GXD which we computed in #6 to be 75°
So m∠BXF = m∠GXD = 75°