Question

2. Given < MCP = 65°, find the measurement of arc MP , arc MRP and < MRP.​

Answer 1

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We know that the Angle subtended by an arc on centre of the circle is double as that of Angle subtended by the same arc on the circumference (boundary) of the circle

So,

• 
  `\sf \angle MCP = 2\angle MRP`

• 
  `\sf65 \degree = 2 \angle MRP`

• 
  `\sf\angle MRP = 65 \degree / 2`

• 
  `\sf\angle MRP = 32.5 \degree`

Answer 2

• arc MP = 65°
• arc MRP = 295°
• angle MRP = 32.5°

Explanation:

The measure of an arc is the same as the measure of the central angle it subtends.

arc MP = ∠MCP = 65°

Long arc MRP is the difference between arc MP and the full circle:

arc MRP = 360° -65° = 295°

Inscribed angle MRP is half the measure of the arc it subtends:

∠MRP = (arc MP)/2 = 65°/2 = 32.5°