Question

Find the angle measure x in the following figure: [3 marks]

Answer 1

First base interior angle = ${180}^{\circ }-{70}^{\circ }={110}^{\circ }$ [0.5 mark]
Second base interior angle = ${180}^{\circ }-{60}^{\circ }={120}^{\circ }$ [0.5 mark]

There are 5 sides, n = 5
$\therefore Anglesumofapolygon=(n-2)\times {180}^{\circ }$ [0.5 mark]
$=(5-2)\times {180}^{\circ }={540}^{\circ }$
$\therefore {30}^{\circ }+x+{110}^{\circ }+{120}^{\circ }+x={540}^{\circ }$ [0.5 mark]
$\Rightarrow {260}^{\circ }+2x={540}^{\circ }\Rightarrow 2x={540}^{\circ }-{260}^{\circ }\Rightarrow x={140}^{\circ }$
[1 mark]