JAMB 1991 · UME · Q31

The angles of a quadrilateral are $5x - 30$ , $4x + 60$ , $60 - x$ and $3x + 61$ . Find the smallest of these angles.

Worked solution (try it first)

The angles of a quadrilateral add up to $360^\circ$ : $(5x - 30) + (4x + 60) + (60 - x) + (3x + 61) = 360$ .
Collect terms: $11x + 151 = 360$ , so $11x = 209$ and $x = 19$ .
The angles are $65^\circ$ , $136^\circ$ , $41^\circ$ and $118^\circ$ .
The smallest is $60 - x$ , option C.