Question

Question

Use the image to answer the 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 HI≅IJ
and m∠KIJ=35
degrees, then what is m∠KGH
?

(1 point)
Responses

17.5 degrees
17.5 degrees

70 degrees
70 degrees

140 degrees
140 degrees

110 degrees

Answer 1

To solve for \( m∠KGH \), we can use the properties of circles and angles.

1. Since \( HI \cong IJ \), this indicates that the segments \( HI \) and \( IJ \) are equal in length. This suggests that triangles formed by these segments would exhibit some symmetry.

2. The angle \( m∠KIJ = 35° \) is given. We can analyze the central angle formed by points \( K \), \( G \), and \( I \).

3. According to the inscribed angle theorem, the measure of an angle formed by two points on a circle and the center of the circle is twice the measure of the inscribed angle subtended by those same points on the circumference.

   \( m∠KGH = \frac{1}{2} m∠KIJ \)

Since \( m∠KIJ = 35° \):

4. Therefore, we can calculate \( m∠KGH \) as follows:

\[ m∠KGH = \frac{1}{2} \cdot 35° = 17.5° \]

So, the correct response is \( \text{17.5 degrees} \).