in the diagram of circle c, what is the measure of ∠1? 17° 35° 70° 71°

Answer:

A. $17^{\circ}$

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Find the measure of the arc intercepted by the angle with measure $36^{\circ}$

Let the arc intercepted by the $36^{\circ}$ angle be $x$. By the inscribed - angle theorem, $36^{\circ}=\frac{1}{2}x$, so $x = 72^{\circ}$.

Step3: Find the measure of the arc intercepted by $\angle1$

The whole circle is $360^{\circ}$. The arc intercepted by $\angle1$ is $106^{\circ}-72^{\circ}=34^{\circ}$.

Step4: Calculate the measure of $\angle1$

By the inscribed - angle theorem, $\angle1=\frac{1}{2}\times34^{\circ}=17^{\circ}$.