NECO 2023 · Paper 2 · Q2

(a)
The sum of the interior angles of a regular polygon is $1440^\circ$ . (i) How many sides has the polygon? (ii) Find the size of each exterior angle.
Separate values with commas, e.g. 3, −2
(b)
Find the principal that will earn ₦29,880.00 in 15 years at $3\%$ per annum simple interest.

Worked solution (try it first)

(a)(i)

The interior angles of an $n$ -sided polygon add up to $(n - 2) \times 180^\circ$ .
So $(n - 2) \times 180 = 1440$ , $n - 2 = 8$ and $n = 10$ .

(ii)

The exterior angles of any polygon add up to $360^\circ$ , so each is $\frac{360^\circ}{10} = 36^\circ$ .

(b)

$I = \frac{PRT}{100}$ : $29\,880 = \frac{P \times 3 \times 15}{100}$
$= 0.45P$ , so $P = \frac{29\,880}{0.45} = ₦66,400$ .

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