Question

information to answer the question.
given;
\\(\overline{cb}\\) is a diameter of the circle.
the measure of minor arc \\(\widehat{ac}\\) is \\(110^\circ\\).
the measure of \\(\angle bck\\) is \\(20^\circ\\).
diagram is not drawn to scale.
what is the measure of \\(\angle ack\\)?
\\(\bigcirc\\) a. \\(15^\circ\\) \\(\bigcirc\\) d. \\(30^\circ\\)
\\(\bigcirc\\) b. \\(20^\circ\\) \\(\bigcirc\\) e. \\(60^\circ\\)
\\(\bigcirc\\) c. \\(25^\circ\\)

Explanation:

Step1: Find arc AB measure

Since $\overline{CB}$ is a diameter, the total arc $ACB$ is $180^\circ$.
$\text{Arc } AB = 180^\circ - \text{Arc } AC = 180^\circ - 110^\circ = 70^\circ$

Step2: Calculate $\angle ACB$

$\angle ACB$ is an inscribed angle over arc $AB$.
$\angle ACB = \frac{1}{2} \times \text{Arc } AB = \frac{1}{2} \times 70^\circ = 35^\circ$

Step3: Compute $\angle ACK$

Subtract $\angle BCK$ from $\angle ACB$.
$\angle ACK = \angle ACB - \angle BCK = 35^\circ - 20^\circ = 15^\circ$

Answer:

A. $15^\circ$