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 angle CGD ?

A.

68°
B.

82°
C.

90°
D.

98°

Answer 1

To find the measure of angle CGD, we will first find the measure of angle BGF and then use that to find the measure of angle CGD.

Since angle FGE is 22 degrees and angle AGB is 60 degrees, we can find angle BGF:

angle BGF = 180 - angle FGE - angle AGB
angle BGF = 180 - 22 - 60
angle BGF = 98 degrees

Now, we know that angles BGF and CGD are vertical angles, which means they are equal in measure:

angle BGF = angle CGD
angle CGD = 98 degrees

So, the measure of angle CGD is 98 degrees. Therefore, the answer is D. 98°.