This figure shows 3 intersecting lines.

Question

Lines A-D, B-E, and C-F intersect at G. The angles F-G-E is 22 degrees, angle A-G-B is 60 degrees.

What is the measure of CGD ?

A.
68°

B.
82°

C.
90°

D.
98°

Answer 1

B. 82°

To find the measure of CGD, notice that angle CGD is a vertical angle to angle AGB (since they are opposite each other where lines B-E and C-F intersect). Therefore, the measure of angle CGD is also 60 degrees.

Since angle FGE + angle AGB + angle CGD add up to 180 degrees (as they form a straight line), we can find the measure of angle FGE + angle CGD:
22 degrees + 60 degrees = 82 degrees

Therefore, the measure of angle CGD is 82 degrees.