To find the measure of an inscribed angle when you know the central angle that intercepts the same arc, we use a simple rule:
The measure of an inscribed angle is half the measure of the central angle.
Formula:
Inscribed Angle = (1/2) × Central Angle
Let’s solve each problem one by one.
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Problem 1:
Central angle ∠AOB = 70°
Inscribed angle ∠ACB intercepts the same arc AB.
So, m∠ACB = (1/2) × 70° =
35°
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Problem 2:
Central angle ∠DOB = 140°
Inscribed angle ∠DAB intercepts the same arc DB.
So, m∠DAB = (1/2) × 140° =
70°
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Problem 3:
Central angle EOG = 80°
Inscribed angle ∠EFG intercepts the same arc EG.
So, m∠EFG = (1/2) × 80° =
40°
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Problem 4:
Central angle ∠MON = 160°
Inscribed angle ∠MPN intercepts the same arc MN.
So, m∠MPN = (1/2) × 160° =
80°
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Problem 5:
Central angle ∠JIK = 90°
Inscribed angle ∠JHK intercepts the same arc JK.
So, m∠JHK = (1/2) × 90° =
45°
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Problem 6:
Central angle ∠SRT = 50°
Inscribed angle ∠SQT intercepts the same arc ST.
So, m∠SQT = (1/2) × 50° =
25°
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Final Answer:
1) 35°
2) 70°
3) 40°
4) 80°
5) 45°
6) 25°
Parent Tip: Review the logic above to help your child master the concept of central and inscribed angles worksheet answers.
