Question

cd is a diameter of circle c. what is m∠cab? 90° 180° 219° 231° 51° 39°

Explanation:

Step1: Recall circle - arc property

The sum of the central - angles of a circle is 360°.

Step2: Identify known angles

We know that \(\angle FCE = 90^{\circ}\), \(\angle ECD=39^{\circ}\), and \(\angle DCB\) is part of the arc we want to find. Also, \(\angle FCG = 51^{\circ}\) and \(\angle GCD\) is a straight - angle (180°) since \(GD\) is a diameter.

Step3: Calculate \(m\widehat{CBA}\)

\(m\widehat{CBA}=360^{\circ}-\angle FCE-\angle ECD - \angle FCG\).
Substitute the values: \(\angle FCE = 90^{\circ}\), \(\angle ECD = 39^{\circ}\), \(\angle FCG=51^{\circ}\).
\(m\widehat{CBA}=360-(90 + 39+51)\)
\(=360 - 180\)
\(= 180^{\circ}\)

Answer:

\(180^{\circ}\)