WAEC 2022 · Paper 1 · Q29

Find, correct to the nearest degree, the acute angle formed by the lines $y = 2x + 5$ and $2y = x - 6$ .

Worked solution (try it first)

The gradients are $m_1 = 2$ and, from $y = \frac12 x - 3$ , $m_2 = \frac12$ .
The acute angle $\theta$ between two lines has $\tan\theta = \left|\dfrac{m_1 - m_2}{1 + m_1 m_2}\right|$
$= \dfrac{1.5}{2}$
$= 0.75$ .
So $\theta = 36.87^\circ \approx 37^\circ$ , option C.