Question

Given circle T, and tangents AD and CD, what is the measure of angle ADC?

Answer 1

The measure of angle ∡ADC is 36°

Explanation:

Here answer the question, we draw C to meet T and A to T to form an angle ∡ATC;

We note that the angle subtended at the center of a circle is two times that of the angle at the circumference, therefore ∡ATC = ∡ABC = 2 × 72 = 144 °

Also ∡TCD = ∡TAD = 90° Angle between radius and a tangent

Therefore, ∡ATC + ∡TCD + ∡TAD + ∡ADC = 360° (Sum of interior angles of a polygon)

Which gives; 144 + 90 + 90 + ∡ADC = 360

∴ ∡ADC = 360 -324 = 36°

The measure of angle ∡ADC = 36°.