Why is this divided by 2? Measure A = 31°. Click picture

ANSWER
[tex]m\angle A = 31 \degree[/tex]
EXPLANATION
This is a Circle Theorem .
The angle created by an arc at the center of a circle is twice the angle created at the circumference by the same arc.
This implies that
[tex]m\angle B=2m\angle A[/tex]
In other words;
[tex] \frac{m\angle \:B }{2} =m\angle A[/tex]
[tex]m\angle B + 298 = 360[/tex]
[tex]m\angle B = 360 - 298 = 62 \degree[/tex]
[tex]\frac{62 }{2} =m\angle A[/tex]
[tex]m\angle A = 32 \degree[/tex]