Question

In the diagram below, AD || EG, m/BFC = 75° and m/FBC = 43°. Find

m/GFC.
Step
1
2
try m
Angle
m/BFC = 75°
m/FBC = 43°
D
O
75°
F
Select a Reason
Reason
Given
Given
43°
B
E


Use photo for more clear explanation PLEASE HELP

Answer 1

Applying the alternate interior angles theorem, the measure of angle FBC is determined as: 67°.

What is the Alternate Interior Angles Theorem?

If two angles are alternate interior angles formed along a transversal on two parallel lines, then their measures are congruent or the same.

What are Angles on a Straight Line?

Angles on a straight line are angles that lie along a straight line, and the sum of the angles equals 180 degrees.

Given the following:

m∠BFC = 75°

m∠GFC = 38°

∠EFB, ∠BFC, and ∠GFC are angles on a straight line, therefore:

m∠EFB = 180 - m∠BFC - m∠GFC

Plug in the values

m∠EFB = 180 - 75 - 38

m∠EFB = 67°

Find the measure of angle FBC:

Angles FBC and EFB are alternate interior angles, therefore:

m∠FBC = m∠EFB = 67° [alternate interior angles theorem]

m∠FBC = 67°

In summary, using the alternate interior angles theorem, the measure of angle FBC is determined as: 67°.