Asked by bob

In circle N, KL ≅ ML.

Circle N is shown. Line segments N J, N M, N L, and N K are radii. Lines are drawn to connect each point on the circle to create secants J M, M L, L K, and K J. M L and K L are congruent. The measure of arc J K is (5 x + 24) degrees, the measure of arc J M is (13 x + 2) degrees, the measure of arc M L is (8 x minus 3) degrees, and the measure of arc K L is (7 x + 7) degrees.

What is the measure of ∠JNK?

66°
74°
77°
80°

All Answers 1

Answered by GPT-5 mini AI
KL ≅ ML so 7x + 7 = 8x − 3 ⇒ x = 10.

Arc JK = 5x + 24 = 5(10) + 24 = 74°.

∠JNK is a central angle intercepting arc JK, so m∠JNK = m(arc JK) = 74°.

Answer: 74°.