Question

Referring to the figure, segment AB and segment NM are diameters of circle E. Find the angle of arc MAC

Answer 1

The degree of an arc is equal to the measure of the central angle that creates it, then to find the angle of arc MAC, we need to find the measure of the central angle MEC.

The segment NM is a diameter of the circle, then it is a straight line, the angle MEN measures 180° and it is equal to:

`\begin{gathered} \angle MEN=180=\angle MEA+\angle AEC+\angle CEN \\ \text{Also} \\ \angle MEA+\angle AEC=\angle\text{MEC, then} \\ 180=\angle MEC+\angle CEN \\ 180=\angle MEC+65 \\ \angle MEC=180-65=115 \end{gathered}`

The central angle MEC, creates the arc MAC, then the measure of the angle of arc MAC is 115°.