Question

Angle PQR is inscribed in arc PQR of a circle with centre O. If angle PQR = 70,Find m(arc PQR)
options:
65
130
220
140
​

Answer 1

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Answer 2

Given is an arc PQR of a circle having an angle PQR of measure $70$°inscribed in it, Find m(arc PQR).

Explanation:

• Here angle PQR is the angle subtended by the chord PR at the circumference of the circle.
• Now angle POR is the angle subtended by the same chord at the center of the circle.
• We know that the measure of the angle subtended at the center is double the angle subtended at the circumference by a chord.
• Hence, $\angle POR=2\angle PQR=140$°
• Now the angle m(arc PQR) is the angle subtended by the arc PQR at the center O.
• Hence, we have  
•                      $m(arc\ PQR)+\angle POR=360\\->m(arc\ PQR)=360-140\\->m(arc\ PQR)=220\ deg.$    
• The measure of m(arc PQR) is the option (c) $220$°.