Question

the perimeter of a certain sector of a circle is equal to the length of the arc of the semicircle having the same radius. the angle of sector (approx) is

Answer 1

Let the radius of a circle be R. The perimeter of the semicircle will consist of the semicircular arc and the diameter or (pi)R+2R. The perimeter of the sector is arc of the sector + 2R. Equating the two we get

(pi)R+2R = arc of the sector + 2R, or

length arc of the sector = (pi)R = R x theta in radians, or

angle subtended by the arc at the centre is pi radians or 180 deg.

Answer 2

Answer:

65° 24` 29`` (approx.)