Investigate the pattern in the circle. △ABC is a right triangle inscribed in circle R such that chord AB is a diameter. Find the measure of ∠ABC if arc BC is 62 degrees. (1 point) Responses ∠ABC is 59 degrees. triangle upper A upper B upper C is 59 degrees. ∠ABC is 118 degrees. triangle upper A upper B upper C is 118 degrees. ∠ABC is 90 degrees. triangle upper A upper B upper C is 90 degrees. ∠ABC is 31 degrees.

Question

GPT-4o mini · Answer

In a circle, if we have a right triangle inscribed where one side is the diameter (AB), it follows that the angle opposite that diameter (∠ACB) must be 90 degrees due to the inscribed angle theorem.

Since arc BC is given as 62 degrees, we can find the angle ∠ABC using the property that the measure of an inscribed angle is half the measure of the arc it intercepts.

Here, arc BC is intercepting angle ∠ABC. Therefore, we calculate:

\[ \angle ABC = \frac{1}{2} \times \text{measure of arc BC} = \frac{1}{2} \times 62^\circ = 31^\circ \]

Thus, ∠ABC measures 31 degrees.

The correct answer is: \(\angle ABC\) is 31 degrees.