Question

Angle G is a circumscribed angle of circle E.

Circle E is shown. Line segments F E and D E are radii. A line is drawn to connect points F and D. Tangents F G and D G intersect at point G outside of the circle. Angles E B D and F D E have measures of x degrees.

What is the measure of angle G, in terms of x?

x° + x°
x° + 90°
180° – x°
180° – 2x°

Answer 1

Answer: x° + x°.

Explanation: In isosceles triangle FDE (EF = ED) the base angles at F and D are both x, so the central angle FED = 180° − 2x. The angle between the two tangents equals 180° − ∠FED, hence angle G = 180° − (180° − 2x) = 2x (i.e. x + x).