Question

in circle o, $overline{ad}$ and $overline{be}$ are diameters. the measure of arc ab is $55^{circ}$ and the measure of arc cd is $25^{circ}$. what is the measure of $widehat{eac}$? 100° 125° 235° 280°

Explanation:

Step1: Recall circle - arc property

The sum of the measures of the arcs of a circle is 360°.

Step2: Identify known arcs

We know that arc $AB = 55^{\circ}$ and arc $CD=25^{\circ}$. Since $\overline{AD}$ and $\overline{BE}$ are diameters, the semi - circle arcs have a measure of 180°.

Step3: Calculate the measure of arc $EAC$

The measure of arc $EAC$ can be found by subtracting the sum of arc $AB$ and arc $CD$ from 360°.
The sum of arc $AB$ and arc $CD$ is $55^{\circ}+25^{\circ}=80^{\circ}$.
Then the measure of arc $EAC$ is $360^{\circ}- 80^{\circ}=280^{\circ}$.

Answer:

280°