In circle H with the measure of minor arc arc, G, J, equals, 30, degrees, comma GJ⌢ =30 ∘ , find m, angle, G, K, J, .m∠GKJ.

1. Break Down the Problem

To find $m\angle GKJ$, we must understand the relationship between an inscribed angle and the arc it subtends in a circle. The angle $GKJ$ is an inscribed angle that intercepts minor arc $GJ$.

2. Relevant Concepts

The inscribed angle theorem states that the measure of an inscribed angle is half the measure of the intercepted arc. The formula can be expressed as: $m\angle GKJ = \frac{1}{2} m(GJ\hat{)}$ where $m(GJ\hat{)}$ is the measure of arc $GJ$.

3. Analysis and Detail

Given that:

• $m(GJ\hat{)} = 30^\circ$

We apply the inscribed angle theorem: $m\angle GKJ = \frac{1}{2} \times m(GJ\hat{)}$

Substituting the value of the arc: $m\angle GKJ = \frac{1}{2} \times 30^\circ = 15^\circ$

4. Verify and Summarize

We derived $m\angle GKJ$ correctly using the inscribed angle theorem. Therefore, the calculated measure of angle $GKJ$ is verified.

Final Answer

$m\angle GKJ = 15^\circ$