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.
Question
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.
Solution
In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. This is known as the Inscribed Angle Theorem.
Given that the measure of minor arc GJ is 30 degrees, the measure of angle GKJ, which intercepts arc GJ, would be half of this.
So, m∠GKJ = 1/2 * m(arc GJ)
Therefore, m∠GKJ = 1/2 * 30 = 15 degrees.
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