7. D. Arc JK = 124°
8. Applying the angle of intersecting chords theorem, m∠1 = 115°.
What is the Angle of Intersecting Chords Theorem?
The angle of intersecting chords theorem states that the angle (∠1) formed by two chords in a circle, equals half of the sum of the intercepted arcs (arcs ML and JK).
Arc JMK = 2(118) = 236° [inscribed angle theorem]
Arc JK = 360 - arc JMK = 360 - 236
Arc JK = 124°
Arc ML = 236 - 70 - 60 = 106°.
m∠1 = 1/2(arc JK + arc ML)
m∠1 = 1/2(124 + 106)
m∠1 = 115°.
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