Use the image to answer the question.

Question

A circle has a center point marked as upper G. Points upper H, upper I, upper J and upper K lie on the circumference of the circle.

If m∠KIJ=37
degrees, then what is the measure of arc IJ
?

(1 point)
Responses

53 degrees
53 degrees

143 degrees
143 degrees

74 degrees
74 degrees

106 degrees

Answer 1

To find the measure of arc IJ given that m∠KIJ = 37 degrees, we can use the fact that an inscribed angle (like ∠KIJ) is half the measure of the arc it intercepts.

The inscribed angle ∠KIJ intercepts the arc IJ, so we can calculate the measure of arc IJ using the formula:

\[ m!arc\ IJ = 2 \times m\angle KIJ \]

Substituting the given value:

\[ m!arc\ IJ = 2 \times 37 = 74 \text{ degrees} \]

Therefore, the measure of arc IJ is 74 degrees.

So the correct response is:

74 degrees.