Question

segments ac and bd are diameters of circle o. what is the measure of arc adb? 107° 146° 253° 287°

Explanation:

Step1: Recall circle - arc relationship

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

Step2: Identify the related arcs

We know that \(\angle AOD = 73^{\circ}\), and the measure of an arc is equal to the measure of its central - angle. The arc \(\overset{\frown}{AD}\) has a measure of 73°.

Step3: Calculate the measure of \(\overset{\frown}{ADB}\)

The arc \(\overset{\frown}{ADB}\) is the major arc. The measure of the whole circle is 360°. The measure of \(\overset{\frown}{ADB}=360^{\circ}-\text{measure of }\overset{\frown}{AB}\). Since \(\angle AOD = 73^{\circ}\), the measure of \(\overset{\frown}{ADB}=360 - 73=287^{\circ}\).

Answer:

287°