If the arc of a circle of radius 30 cm has a length of 19 cm then the angle subtended at the center of the circle is (give an answer in Degree measure)

The angle subtended at the centre O by the arc of length 19 cm and radius 30 cm is 36.27°.

Step-by-step explanation:

The radius of the circle, r = 30 cm

The length of the arc of the circle, l = 19 cm

The formula for the arc length of a circle is given by,

l = 2πr * [θ/360°] ... [Here θ = angle subtended at the centre O by the arc]

Now, substituting the given values in the above formula, we get

19 = 2 * (22/7) * 30 * [θ/360°]

⇒ 19 = 188.57 * [θ/360°]

⇒ θ = [360 * 19] / [188.57]

⇒ θ = 36.27°

Thus, the angle subtended by the arc at the centre O is 36.27°.