A circle with a radius of 61cm is made from a wire. The wire is used to make a sector with a radius of 88cm. What is the angle subtended by the sector?

The circle has a radius of 61 cm, therefore its circumference is

C = 2π*61 = 122π cm

If the wire forms sector with a radius of 88 cm (as shown in the figure), then the length of the circular sector is

S = 122π - 2*88 = 207.2743 cm

Because the central angle is θ radians, therefore

88*θ = 207.2743

θ = 2.3554 radians

= (2.3554 rad) * (180 deg/rad)

= 134.95°

Answer:

The angle subtended by the sector is 135° (nearest whole number)