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°
