Given:
Measure of arc FJ = 84°
Measure of arc GH = 76°
To find:
The measure of angle HKJ.
Solution:
Angles inside the circle theorem:
If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the intercepted arc and its vertical arc.
[tex]$\Rightarrow m\angle GKH=\frac{1}{2}(m \ (ar GH) + m \ (ar FJ))[/tex]
[tex]$\Rightarrow m\angle GKH=\frac{1}{2}(84^\circ+76^\circ)[/tex]
[tex]$\Rightarrow m\angle GKH=\frac{1}{2}(160^\circ)[/tex]
[tex]$\Rightarrow m\angle GKH=80^\circ[/tex]
Sum of the adjacent angles in a straight line is 180°.
⇒ m∠GKH + m∠HKJ = 180°
⇒ 80° + m∠HKJ = 180°
Subtract 80° from both sides.
⇒ 80° + m∠HKJ - 80° = 180° - 80°
⇒ m∠HKJ = 100°
The measure of ∠HKJ is 100°.
