Find the angle subtended at the centre of a

We know that the arc length l of a sector of an angle θ in a circle of radius r is

$l=\frac{\theta}{360^{\circ}} \times 2 \pi r$

It is given $l=\frac{a \pi}{4} \mathrm{~cm}$ and radius $r=a \mathrm{~cm}$.

Now we substitute the value of l and r in above formula to find the value of angle θ subtended at the centre of circle.

$\frac{a \pi}{4} \mathrm{~cm}=\frac{\theta}{360^{\circ}} \times 2 \pi \times a$

$\theta=\frac{a \pi \times 360^{\circ}}{2 \pi a \times 4}$

$\theta=45^{\circ}$