WAEC 2024 · Paper 2 · Q11

(a)
Find the equation of the line that passes through the origin and the point of intersection of the lines $x + 2y = 7$ and $x - y = 4$ . (Give $y$ in terms of $x$ .)
(b)
The ratio of an interior angle to an exterior angle of a regular polygon is $4 : 1$ . Find the: (i) size of an exterior angle; (ii) number of sides; (iii) sum of the interior angles of the polygon.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Find where the lines cross.
Take $x - y = 4$ from $x + 2y = 7$ : $3y = 3$ , so $y = 1$ and $x = 4 + 1 = 5$ .
The point is $(5, 1)$ .
The line passes through $(0, 0)$ and $(5, 1)$ : gradient $= \frac{1 - 0}{5 - 0} = \frac15$ .
Through the origin, $y = \frac15 x$ , that is $x - 5y = 0$ .