Question

question 2 of 10
what is the measure of \\( \angle j g k \\) shown in the diagram below?
a. \\( 112^{circ} \\)
b. \\( 56^{circ} \\)
c. \\( 138^{circ} \\)
d. \\( 69^{circ} \\)

Explanation:

Step1: Recall the formula for the measure of an angle formed by two secants

The measure of an angle formed by two secants outside a circle is $\frac{1}{2}$ (difference of the measures of the intercepted arcs). The formula is $m\angle JGK=\frac{1}{2}(m\overarc{JK}-m\overarc{HI})$.

Step2: Substitute the values of the arcs

We are given that $m\overarc{JK} = 125^{\circ}$ and $m\overarc{HI}=13^{\circ}$. Substitute these values into the formula: $m\angle JGK=\frac{1}{2}(125 - 13)$.

Step3: Calculate the value

First, find the difference inside the parentheses: $125-13 = 112$. Then, multiply by $\frac{1}{2}$: $\frac{1}{2}\times112=56$.

Answer:

B. \(56^{\circ}\)