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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

143 degrees
143 degrees

106 degrees
106 degrees

74 degrees
74 degrees

53 degrees
53 degrees

Answer 1

To find the measure of arc IJ when given the measure of angle KIJ, we can use the Inscribed Angle Theorem. According to this theorem, an inscribed angle is half the measure of the arc that it intercepts.

In this case, m∠KIJ = 37 degrees, which intercepts arc IJ. Therefore, to find the measure of arc IJ, we can use the following formula:

\[ m \text{ arc IJ} = 2 \times m∠KIJ \]

Calculating this gives us:

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

Hence, the measure of arc IJ is 74 degrees.