JAMB 2010 · UTME · Q29

Angles, triangles & polygons

The interior angles of a quadrilateral are $(x + 15)^\circ$ , $(2x - 45)^\circ$ , $(x - 30)^\circ$ and $(x + 10)^\circ$ . Find the value of the least interior angle.

Worked solution (try it first)

The angles of a quadrilateral add up to $360^\circ$ : $(x + 15) + (2x - 45) + (x - 30) + (x + 10) = 360$ .
Collect terms: $5x - 50 = 360$ , so $5x = 410$ and $x = 82$ .
The angles are $97^\circ$ , $119^\circ$ , $52^\circ$ and $92^\circ$ .
The least is $52^\circ$ , option B.

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