Question

Who can solve this problem?!!!

Answer 1

`m \overset\frown{DEB}=236^(\circ)`

Explanation:

Angles around a point sum to 360°.

Therefore, we can calculate the measure of angle DEB by subtracting the measures of angles DOC and COB from 360°:

`\begin{aligned}m \angle DOC + m\angle COB + m \angle DEB &= 360^(\circ)\\44^(\circ)+ 80^(\circ)+m \angle DEB &= 360^(\circ)\\124^(\circ)+m \angle DEB &= 360^(\circ)\\124^(\circ)+m \angle DEB -124^(\circ)&= 360^(\circ)-124^(\circ)\\m \angle DEB &= 236^(\circ)\end{aligned}`

The measure of an arc is equal to the measure of its corresponding central angle. Therefore, the measure of arc DEB is equal to the measure of the central angle DEB. As m∠DEB = 236°, then:

`m \overset\frown{DEB}=236^(\circ)`