Question

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

Answer 1

Since AB and NM are the diameters, we can conclude that E is the central point. Therefore, the angle AEC (Central angle) is equal to the arc.

∠MEA, ∠AEC and ∠NEC are supplementary angles, therefore:

$\begin{gathered} \angle MEA+\angle AEC+\angle NEC=180 \\ 55+\angle AEC+65=180 \\ 120+\angle AEC=180 \\ so\colon \\ \angle AEC=180-120 \\ \angle AEC=60 \\ _{\text{ }}Therefore\colon \\ AC=\angle AEC \\ AC=60 \end{gathered}$

Answer:

60⁰