Question

find the measure of arc fjh and ( mangle fgh ).
measure of arc fjh: select
( mangle fgh ): select

Explanation:

Step1: Find measure of arc FJH

A circle has a total of \( 360^\circ \). The given arc (the minor arc between F and H) is \( 101^\circ \). Arc FJH is the major arc, so we subtract the minor arc from \( 360^\circ \).
\[
\text{Measure of arc } FJH = 360^\circ - 101^\circ = 259^\circ
\]

Step2: Find \( m\angle FGH \)

The formula for the measure of an angle formed by two tangents (or a tangent and a secant, but here it's two tangents from point G to the circle) is \( m\angle = \frac{1}{2}(\text{measure of major arc} - \text{measure of minor arc}) \). Wait, actually, for two tangents, the angle is \( \frac{1}{2}(\text{major arc} - \text{minor arc}) \), but also, since the sum of the angle and the minor arc's related angle? Wait, no, the correct formula is that the measure of the angle formed by two tangents is \( \frac{1}{2}(\text{measure of the major arc} - \text{measure of the minor arc}) \). But also, we know that the angle between two tangents and the minor arc: the angle \( \angle FGH \) and the minor arc \( FH \) (101°) have the relationship \( m\angle FGH = \frac{1}{2}(\text{major arc} - \text{minor arc}) \), but major arc is 259°, minor is 101°, so \( \frac{1}{2}(259 - 101) = \frac{1}{2}(158) = 79^\circ \). Alternatively, since the tangents are perpendicular to the radii, but maybe easier: the angle between two tangents is supplementary to the central angle of the minor arc? Wait, no, the central angle for arc FH is 101°, and the angle between two tangents: the sum of the angle at G and the central angle? No, the correct formula is \( m\angle FGH = \frac{1}{2}(\text{measure of major arc} - \text{measure of minor arc}) \). Let's compute that: major arc is 259, minor is 101, so 259 - 101 = 158, half of that is 79. So \( m\angle FGH = 79^\circ \).

Answer:

Measure of arc \( FJH \): \( 259^\circ \)
\( m\angle FGH \): \( 79^\circ \)