Logan is reading about architecture and learns that trusses can be used to support roofs.
He wants to find the measures of the angles on a truss.

A drawing of a roof support system with multiple triangles shown. One small triangle is A B F, another small triangle is B C F. These two triangles together form triangle A C F. One small triangle is C F G. Another small triangle is C D G. Together these triangles form quadrilateral C D G F.

Part A
The measure of ∠AFC is 120°, and the measure of ∠BFC is 95°. Which equation can you use to find the measure of ∠AFB?
120° + 95° = x
120° – 95° = x
120° + x = 95°
x – 120° = 95°
Part B
The measure of ∠AFC is 120°, and the measure of ∠BFC is 95°.
What is the measure of ∠AFB?

Part C
The measure of ∠BCF is 60°, and the measure of ∠FCG is 35°. Which equation can you use to find the measure of ∠BCG?
60° + 35° = x
60° – 35° = x
60° + x = 35°
35° + x = 60°
Part D
The measure of ∠BCF is 60°, and the measure of ∠FCG is 35°. What is the measure of ∠BCG?

To find the measure of ∠AFB, we can use the fact that angles on a straight line add up to 180°. Since ∠AFC is 120° and ∠BFC is 95°, we can calculate ∠AFB by subtracting the sum of ∠AFC and ∠BFC from 180°:

180° - (120° + 95°) = 180° - 215° = -35°

Therefore, the measure of ∠AFB is 35°.

Part B:

The measure of ∠AFB is 35°.

Part C:

To find the measure of ∠BCG, we need to consider that angles around a point add up to 360°. Given that ∠BCF is 60° and ∠FCG is 35°, we can calculate ∠BCG by subtracting the sum of these two angles from 360°:

360° - (60° + 35°) = 360° - 95° = 265°

Therefore, the measure of ∠BCG is 265°.

Part D:

The measure of ∠BCG is 265°.

Step-by-step explanation: