Question

match the arc or central angle to the correct measure based on the figure below.
a. m\\(widehat{ifg}\\)
b. m\\(widehat{hi}\\)
c. m\\(\angle gjh\\)
d. m\\(widehat{gih}\\)

1. 50°
2. 130°
3. 230°
4. 180°

Explanation:

Step1: Recall arc - central angle relationship

The measure of a central angle is equal to the measure of its intercepted arc. The sum of the measures of arcs in a circle is 360°.

Step2: Analyze $\overset{\frown}{FG}$

Since the given angle is 130°, assume $\angle FJG = 130^{\circ}$, then $m\overset{\frown}{FG}=130^{\circ}$.

Step3: Find $m\overset{\frown}{HI}$

The diameter divides the circle into two semi - circles. If we assume that one of the non - given arcs formed by the intersection of diameters is 130°, then the arc $\overset{\frown}{HI}$ which is a semi - circle has a measure of 180°. So $m\overset{\frown}{HI}=180^{\circ}$.

Step4: Determine $m\angle GJH$

$\angle GJH$ and the 130° angle are supplementary. So $m\angle GJH=180 - 130=50^{\circ}$.

Step5: Calculate $m\overset{\frown}{GIH}$

The measure of the major arc $\overset{\frown}{GIH}$ is $360 - 130=230^{\circ}$.

Answer:

a. 2. 130°
b. 4. 180°
c. 1. 50°
d. 3. 230°