Question

in circle g with $m\angle fgh = 106^\circ$, find the $m\angle fjh$.

Explanation:

Step1: Identify angle relationship

The central angle $\angle FGH$ intercepts arc $FH$, and the inscribed angle $\angle FJH$ intercepts the same arc. The measure of an inscribed angle is half the measure of its intercepted central angle.

Step2: Calculate inscribed angle

$$m\angle FJH = \frac{1}{2} \times m\angle FGH$$
Substitute $m\angle FGH = 106^\circ$:
$$m\angle FJH = \frac{1}{2} \times 106^\circ$$

Answer:

$53^\circ$