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mario62 [17]
2 years ago
13

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

Mathematics
1 answer:
zysi [14]2 years ago
3 0

Answer:

The measure of angle HJK is 36°

Step-by-step explanation:

<em><u>In a circle</u></em>, <em>the measure of the inscribed angle equal half the measure of the central angle subtended by the same arc</em>

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 = \frac{1}{2} m∠HJK

∵ m∠HLK = 18°

∴ 18 = \frac{1}{2} m∠HJK

→ Multiply both sides by 2

∴ 36 = m∠HJK

∴ The measure of angle HJK is 36°

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