Question

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

Answer 1

ANSWER

$m\angle A = 31 \degree$

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

$m\angle B=2m\angle A$

In other words;

$\frac{m\angle \:B }{2} =m\angle A$

$m\angle B + 298 = 360$

$m\angle B = 360 - 298 = 62 \degree$

$\frac{62 }{2} =m\angle A$

$m\angle A = 32 \degree$