In the circle with centre $O$, the shaded sector represents $20 \%$

of the area of the circle. What is the size of angle $A O B$ ?
(A) $36^{\circ}$
(D) $80^{\circ}$
(B) $72^{\circ}$
(C) $90^{\circ}$
(E) $70^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-103.jpg?height=223&width=223&top_left_y=1466&top_left_x=1447)
In the circle with centre $O$, the shaded sector represents $20 \%$ of the area of the circle. What is the size of angle $A O B$ ?
(A) $36^{\circ}$
(B) $72^{\circ}$
(C) $90^{\circ}$
(D) $80^{\circ}$
(E) $70^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-468.jpg?height=352&width=355&top_left_y=1228&top_left_x=1357)

## Solution

If the area of the sector represents $20 \%$ of the area of the circle then angle $A O B$ is $20 \%$ of $360^{\circ}$ or $72^{\circ}$.

ANSWER: (B)