Find the measure of the arc or central angle indicated. Assume that the lines which’s appear to be diameters are actual diameters.

m∠HKF = 87°

Solution:

Given data:

m(ar JF) = 135° and m(ar GH) = 42°

GJ is the diameter of the circle.

Angle in a diameter is 180°.

⇒ m(ar JF) + m(ar FG) = 180°

⇒ 135° + m(ar FG) = 180°

Subtract 135° from both sides of the equation.

⇒ m(ar FG) = 45°

⇒ m(ar FGH) = m(ar FG) + m(ar GH)

⇒ m(ar FGH)= 45° + 42°

⇒ m(ar FGH) = 87°

The measure of the central angle is congruent to the measure of the intercepted arc.

⇒ m∠HKF = m(ar FGH)

⇒ m∠HKF = 87°

c. (3,2,6) is the answer.

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step-by-step explanation:

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