Question

Find the degree measure of the angle subtended at the centre of a circle of diameter 60cm by an arc of length 16.5 cm.

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Answer 1

Given , Diameter,d= 60cm

So , radius, r = 30 cm

And, length of arc = 16.5

Now angle subtended by the arc be X

$\frac{x}{360} 2\pi \: r = 16.5 \\ \\ = > \frac{x}{180} \pi \: r = 16.5 \\ \\ = > x = \frac{16.5 \times 180}{\pi \: r} \\ \\ = > x = \frac{16.5 \times 180}{3.14 \times 30} \\ \\ = > x = \frac{16.5 \times 6}{3.14} \\ \\ = > x = 31$

The measurement of the angle is approximately

31° .