Question

In circle G with the measure of minor arc FH = 106, find m

Answer 1

measure of angle FJH = 53

Explanation:

inscribed angle is half the intercepted arc

Answer 2

The measure of m<FJH is 53 degrees

Inscribed angles formed in a circle are half the measure of their intercepted arcs.

This property holds true when the vertex of the inscribed angle lies on the circle and the angle intercepts the arc on the circumference.

For example, if an inscribed angle in a circle measures 60 degrees, then the arc it intercepts measures 120 degrees. This relationship remains consistent regardless of the angle or arc measure, as long as the angle is inscribed in the circle and its vertex lies on the circle itself.

From the diagram shown, we have that;

Intercepted arc = FH = 106 degrees

Then, <FHJ = FH/2 = 106/2 = 53 degrees