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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

53 degrees
53 degrees

74 degrees
74 degrees

143 degrees
143 degrees

106 degrees

Answer 1

To find the measure of arc IJ, we can use the relationship between an inscribed angle and the arc it intercepts. The measure of an arc is twice the measure of the inscribed angle that subtends that arc.

Given that \( m∠KIJ = 37^\circ \), the arc IJ would be measured as follows:

\[ m \text{ arc } IJ = 2 \times m∠KIJ = 2 \times 37^\circ = 74^\circ \]

Therefore, the measure of arc IJ is 74 degrees.