Answer:
The measure of angle HJK is 36°
Step-by-step explanation:
In a circle, the measure of the inscribed angle equal half the measure of the central angle subtended by the same arc
In circle J
∵ J is the center of the circle
∵ H and K lie on the circle
∴ ∠HJK is a central angle subtended by arc HK
∵ L lies on the circle
∴ ∠HLK is an inscribed angle subtended by arc HK
→ By using the rule above
∵ ∠HJK and ∠HLK are the central angle and inscribed angle
subtended by the same arc HK
∴ m∠HLK = [tex]\frac{1}{2}[/tex] m∠HJK
∵ m∠HLK = 18°
∴ 18 = [tex]\frac{1}{2}[/tex] m∠HJK
→ Multiply both sides by 2
∴ 36 = m∠HJK
∴ The measure of angle HJK is 36°
