Question

Point upper D is plotted on the circumference in the upper right; upper F is on the upper left; upper G is on the lower left directly across from upper D, and upper E is on the lower right. A diameter connects upper G upper O upper D. A radius connects upper F upper O. A chord connects upper G upper E. A chord connects upper F upper E.

If m∠FOG=105
𝑚
∠
𝐹
𝑂
𝐺
=
105
degrees, then what is the measure of ∠FOD
∠
𝐹
𝑂
𝐷
?

(1 point)
Responses

85 degrees
85 degrees

37.5 degrees
37.5 degrees

75 degrees
75 degrees

150 degrees

Answer 1

75 degrees

Reason: G and D are endpoints of a diameter, so OG and OD are opposite rays. Thus ∠FOG and ∠FOD are a linear pair and sum to 180°. So ∠FOD = 180° − 105° = 75°.