Question

in circle g with $m\angle fjh = 63^\circ$, find the $m\angle fgh$.

Explanation:

Step1: Identify angle types

$\angle FJH$ is an inscribed angle, $\angle FGH$ is a central angle, both subtending arc $FH$.

Step2: Apply central angle theorem

The measure of a central angle is twice the measure of its subtended inscribed angle.
$m\angle FGH = 2 \times m\angle FJH$

Step3: Substitute given value

$m\angle FGH = 2 \times 63^\circ$

Answer:

$126^\circ$