Question

Need help please. Not sure how to do this

Answer 1

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.

$\Rightarrow m\angle GKH=\frac{1}{2}(m \ (ar GH) + m \ (ar FJ))$

$\Rightarrow m\angle GKH=\frac{1}{2}(84^\circ+76^\circ)$

$\Rightarrow m\angle GKH=\frac{1}{2}(160^\circ)$

$\Rightarrow m\angle GKH=80^\circ$

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°.