Question

point d is the incenter of triangle bca. if m∠fdg = 128°, what is the measure of ∠fhg? 32° 52° 64°

Explanation:

Step1: Recall the angle - relationship theorem

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc. Here, $\angle FHG$ is an inscribed angle and $\angle FDG$ is a central angle subtending the same arc $\overset{\frown}{FG}$.

Step2: Calculate the measure of $\angle FHG$

Let $m\angle FHG = x$ and $m\angle FDG=y$. We know that $x=\frac{1}{2}y$. Given $y = 128^{\circ}$, then $x=\frac{128^{\circ}}{2}$.
$x = 64^{\circ}$

Answer:

$64^{\circ}$