If the arc of a circle of radius 30 cm has a length of 19 cm, then the angle (in degrees, rounded off to two decimal places) subtended at the centre of the circle is: Take $π =\frac{22}{7}$

36.27

Formula Used

Arc length of a circle , I = 2\(\Pi \)r x \(\theta \)/360

Calculation

Putting values in the formula, we get

= 19 = 2 x \(\frac{22}{7}\) x 30 x \(\theta \)/360

= \(\theta \)/360 = \(\frac{19 \;×\; 7}{44\;×\;30}\)

= \(\theta \) = \(\frac{133}{44\;×\;30}\) x 360 = \(\frac{133\;×\;12}{44}\) = \({36.27}^\circ\)

Therefore, the angle subtended at the center is \({36.27}^\circ\).