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 marks)
Second base interior angle = ${180}^{\circ }-{60}^{\circ }={120}^{\circ }$ (0.5 marks)

There are 5 sides, n = 5
$\therefore Anglesumofapolygon=(n-2)\times {180}^{\circ }$ (0.5 marks)
$=(5-2)\times {180}^{\circ }={540}^{\circ }\therefore {30}^{\circ }+x+{110}^{\circ }+{120}^{\circ }+x={540}^{\circ }\Rightarrow {260}^{\circ }+2x={540}^{\circ }\Rightarrow 2x={540}^{\circ }-{260}^{\circ }\Rightarrow x={140}^{\circ }$ (1.5 marks)