segments ac and bd are diameters of circle o. what is the measure of arc adb? 107° 146° 253° 287°
segments ac and bd are diameters of circle o. what is the measure of arc adb? 107° 146° 253° 287°
Answer
Explanation:
Step1: Recall circle - arc relationship
The sum of the measures of the arcs of a circle is 360°.
Step2: Identify the related arc
The arc $\overset{\frown}{AB}$ has a central - angle measure of 73°. The arc $\overset{\frown}{ADB}$ and $\overset{\frown}{AB}$ are related such that $\overset{\frown}{ADB}+\overset{\frown}{AB}=360^{\circ}$.
Step3: Calculate the measure of $\overset{\frown}{ADB}$
Let $m\overset{\frown}{ADB}=x$. Then $x + 73^{\circ}=360^{\circ}$. Solving for $x$, we get $x=360^{\circ}-73^{\circ}=287^{\circ}$.
Answer:
$287^{\circ}$