in circle o, $overline{ac}$ and $overline{bd}$ are diameters. what is $mwidehat{ab}$? 72° 108° 120° 144°
in circle o, $overline{ac}$ and $overline{bd}$ are diameters. what is $mwidehat{ab}$? 72° 108° 120° 144°
Answer
Answer:
108°
Explanation:
Step1: Recall circle - angle property
The sum of central angles in a circle is 360°.
Step2: Set up an equation
Since AC and BD are diameters, we have 5x = 360 - 180 (the two - right - angle formed by diameters). So 5x=180, then x = 36.
Step3: Calculate m∠AOB
m∠AOB = 3x. Substitute x = 36 into it, we get m∠AOB=3×36 = 108°. And the measure of arc AB is equal to the measure of its central angle ∠AOB, so mAB = 108°.