Question

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm .

Answer 1

The radius of the circle is 100 cm .

The length of the arc is 22 cm .

The angle subtended at the centre of the circle is

Angle subtended= Length of arc Radius of the circle = 22 100 =0.22 radians

We know,

180°=π radians 1 radian=( 180° π )

Multiply both sides of the equation by 0.22 .

0.22 radian=( 0.22×180° π ) =( 0.22×180° 22 7 ) =( 7×180° 100 ) =12.6°

Thus, the angle subtended at the centre of a circle of radius is 12.6° .