Question

gd is a diameter of circle c. what is m\widehat{geb}? 90° 180° 219° 231°

Explanation:

Step1: Recall the total degrees in a circle

A full - circle has \(360^{\circ}\).

Step2: Find the measure of the arc opposite to \(\widehat{GEB}\)

The arc opposite to \(\widehat{GEB}\) has a central - angle measure of \(51^{\circ}+90^{\circ}+39^{\circ}\).

$$51^{\circ}+90^{\circ}+39^{\circ}=(51 + 39)+90^{\circ}=90^{\circ}+90^{\circ}=135^{\circ}$$

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

Since \(m\widehat{GEB}+(51^{\circ}+90^{\circ}+39^{\circ}) = 360^{\circ}\) (the sum of arcs in a circle is \(360^{\circ}\)), then \(m\widehat{GEB}=360^{\circ}-(51^{\circ}+90^{\circ}+39^{\circ})\).
Another way:
We know that the measure of an arc is equal to the measure of its central angle.
The central angle for \(\widehat{GEB}\) is \(360^{\circ}-(51^{\circ}+90^{\circ}+39^{\circ})\)

$$360-(51 + 90+39)=360 - 180=231^{\circ}$$

Answer:

\(231^{\circ}\)