Question

use the drop - down menus to complete the statements about the dia
the measure of arc ab is
the measure of ∠boc is
the measure of arc adc is

Explanation:

Step1: Recall central - angle and arc - measure relationship

The measure of an arc is equal to the measure of its central angle. Given that the central angle of arc $\overset{\frown}{AB}$ is $\angle AOB = 110^{\circ}$, so the measure of $\overset{\frown}{AB}$ is $110^{\circ}$.

Step2: Find the measure of $\angle BOC$

The sum of angles around a point is $360^{\circ}$. We know $\angle AOB=110^{\circ}$ and another angle is $36^{\circ}$. Let $\angle BOC = x$. Then $110^{\circ}+36^{\circ}+x = 360^{\circ}$. Solving for $x$, we get $x=360^{\circ}-(110^{\circ} + 36^{\circ})=214^{\circ}$.

Step3: Find the measure of $\overset{\frown}{ADC}$

The measure of a major arc is $360^{\circ}$ minus the measure of the corresponding minor arc. The minor arc $\overset{\frown}{AC}$ has a central - angle measure of $110^{\circ}+36^{\circ}=146^{\circ}$. So the measure of $\overset{\frown}{ADC}=360^{\circ}-146^{\circ}=214^{\circ}$.

Answer:

The measure of $\overset{\frown}{AB}$ is $110^{\circ}$.
The measure of $\angle BOC$ is $214^{\circ}$.
The measure of $\overset{\frown}{ADC}$ is $214^{\circ}$.