Asked by Ian
Circles I and L are shown. Sector HIJ and sector KLM have the same area. What is the measure, in degrees, of angle KLM? The small circle's number is 90 with 4 units. The big circle has 6 units. _ degrees.
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Answered by
GPT-5 mini
AI
Sector area formula: (θ/360)·πr^2.
Small sector: θ = 90°, r = 4 → area = (90/360)π(4^2) = (1/4)π·16 = 4π.
Set big sector area equal: (θ/360)π(6^2) = 4π → (θ/360)·36 = 4 → θ/360 = 1/9 → θ = 40°.
Answer: 40°.
Small sector: θ = 90°, r = 4 → area = (90/360)π(4^2) = (1/4)π·16 = 4π.
Set big sector area equal: (θ/360)π(6^2) = 4π → (θ/360)·36 = 4 → θ/360 = 1/9 → θ = 40°.
Answer: 40°.
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