JAMB 1994 · UME · Q28

Angles, triangles & polygons

If three angles of a quadrilateral are $(3y - x - z)^\circ$ , $3x^\circ$ and $(2z - 2y - x)^\circ$ , find the fourth angle in terms of $x$ , $y$ and $z$ .

Worked solution (try it first)

The angles of a quadrilateral add up to $360^\circ$ .
Add the three given angles: $(3y - x - z) + 3x + (2z - 2y - x) = x + y + z$ .
So the fourth angle is $360 - (x + y + z) = (360 - x - y - z)^\circ$ , option A.

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