Circle C is intersected by tangent lines GH and JH. The two tangent lines intersect each other at point H. Identify the measure of ∠GHJ if m∠GCJ is 134°.(1 point)

Question

Responses

67°
67°

46°
46°

134°
134°

226°

Answer 1

To solve for the measure of ∠GHJ given that m∠GCJ is 134°, we can use the properties of tangent lines and angles formed by them.

When two tangent lines intersect outside a circle, the angle formed between the lines (in this case ∠GHJ) is equal to half the difference of the measures of the arcs they intercept. The arc they intercept from point G to point J is the arc associated with angle ∠GCJ.

However, in this case, we can directly infer that ∠GHJ is related to the angle made by the tangent line and the straight line drawn through the center of the circle (that meets at an external point).

Since m∠GCJ is 134°, we can calculate ∠GHJ as follows:

\(\angle GHJ = 180^\circ - \angle GCJ\)

Substituting the value of \(\angle GCJ\):

\[ \angle GHJ = 180^\circ - 134^\circ = 46^\circ \]

Thus, the measure of ∠GHJ is 46°.

The correct response is:

46°