Question

Two tangents are drawn to a circle from an external point. If the measure of the major arc is 260º, what is the measure, in degrees, of the angle formed by the two tangents?

Answer 1

80degrees

Explanation:

Using the expression to get the minor arc;

minor arc + major arc = 360degrees

minor arc + 260 = 360

minor arc = 360 - 260

minor arc = 100degrees (central angle)

Note that the central angle and that formed from the intersection of the tangents (X) are supplementary. Hence;

100 + X = 180

X = 180 - 100

X = 80degrees