# Math Help - word problem

1. ## word problem

A circular wire of radius 15cm is cut and bent so as to lie along the circumference of a loop of radius 120cm .Write the measure of the angle subtended by it at the center of the loop.

Thanks

2. Draw a picture first, so you see what it's asking.

2 pi times 15cm is the arc length of a circle radius 120 cm subtended by angle A.

The full circle ix 2 pi and the full circumference is 2 pi times 120.

Thus it's $\frac {2 \pi \times 15}{2 \pi \times 120}$ and that's in radians, so you need to multiply by $\frac {180} {\pi}$ to get the number of degrees.

3. This is how I read this problem, there are 2 circles.

One has a radius of 15cm which gives a circumference of $30\pi$

The other has radius of 120cm which gives a circumference of $240\pi$

The angle will be the proportion of the circumference of circle 1 around the circumference of circle 2

Spoiler:
$\frac{30\pi}{240\pi}\times 360$

4. Originally Posted by Matt Westwood
15cm is the arc length of a circle radius 120 subtended by angle A.

The full circle ix 2 pi and the full circumference is 2 pi times 120.