Question

In circle J with mZHLK = 18, find the mZHJK.

Answer 1

The measure of angle HJK is 36°

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 =
`(1)/(2)` m∠HJK

∵ m∠HLK = 18°

∴ 18 =
`(1)/(2)` m∠HJK

→ Multiply both sides by 2

∴ 36 = m∠HJK

∴ The measure of angle HJK is 36°