Answer:
Step-by-step explanation:
Assuming that
is a diameter, and that the angle of an arc subtending the central angle is congruent,
.
And according to the arc addition postulate,
.
Using the substitution property:
.
Given that
.
Using the substitution property and that the measures apply to the arc addition postulate,
.
.
.
Since
and
are subtending the center of the circle, they form vertical angles and are therefore congruent.

According to the definition of a vertical angle,
.
Using the arc addition postulate again,

Using substitution, as well as how we are given that the central angle subtended by
= 83°, we can find that:
