Question

AD and CD are tangents to the circle below Calculate the size of angle 0

Answer 1

Answer: $59^{\circ}$

Step-by-step explanation:

In triangle ABC, we know that $\angle ABC=130^{\circ}-\theta$. So, by the inscribed angle theorem, minor arc AC is equal to $260^{\circ}-2\theta$.

Thus, major arc AC is equal to $100^{\circ}+2\theta$.

Using the fact that the angle formed by the two tangents is 38 degrees,

$\frac{(100^{\circ}+2\theta)-(260^{\circ}-2\theta)}{2}=38^{\circ}\\\\100^{\circ}+2\theta-260^{\circ}+2\theta=76^{\circ}\\\\4\theta-160^{\circ}=76^{\circ}\\\\4\theta=236^{\circ}\\\\\theta=\boxed{59^{\circ}}$