If the angle subtended by a chord at the center is $150^\circ$, What is the angle subtended at a point on the circle in the same segment?
If the angle subtended by a chord at the center is $150^\circ$, What is the angle subtended at a point on the circle in the same segment?
यदि केंद्र पर एक जीवा द्वारा बनाया गया कोण $150^\circ$ है, तो उसी वृत्तखंड में वृत्त पर एक बिंदु पर बनाया गया कोण क्या होगा?
Detailed Solution & Logic
Correct Answer:
$75^\circ$
Given:
केंद्र पर बना कोण = $150^\circ$
Step 1: Concept
वृत्त में, किसी chord द्वारा केंद्र पर बना कोण = उसी chord द्वारा वृत्त पर बने कोण का 2 गुना होता है।
Step 2: Relation
$\angle \text{(circle)} = \frac{1}{2} \times \angle \text{(center)}$
Step 3: Calculation
$\angle = \frac{150^\circ}{2} = 75^\circ$
Final Answer:
👉 $75^\circ$
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