Acircle 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°

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