in circle o, $overline{ad}$ and $overline{be}$ are diameters. the measure of arc ab is $55^{circ}$ and the…

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°

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°

Answer

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}), and (\overline{AD}) and (\overline{BE}) are diameters. A diameter divides a circle into two semi - circles with an arc 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°. [m\overset{\frown}{EAC}=360^{\circ}-(m\overset{\frown}{AB} + m\overset{\frown}{CD})] [m\overset{\frown}{EAC}=360^{\circ}-(55^{\circ}+ 25^{\circ})] [m\overset{\frown}{EAC}=360^{\circ}-80^{\circ}] [m\overset{\frown}{EAC}=280^{\circ}]

Answer:

280°