Question

question 4 of 10
given ⊙o below, if (widehat{gh}) and (widehat{hj}) are congruent, what is the measure of (angle goh)?

a. (150^circ)
b. (300^circ)
c. (60^circ)
d. (120^circ)

Explanation:

Step1: Recall circle arc-angle rule

Congruent arcs have congruent central angles.

Step2: Calculate total remaining angle

The total degrees in a circle is $360^\circ$. Subtract the given $\angle GOJ = 60^\circ$:
$360^\circ - 60^\circ = 300^\circ$

Step3: Split remaining angle equally

Since $\overset{\frown}{GH} \cong \overset{\frown}{HJ}$, their central angles are equal. Divide the remaining angle by 2:
$\angle GOH = \frac{300^\circ}{2} = 150^\circ$

Answer:

A. $150^\circ$