Question

In the figure given below, PTU is a straight line.

What is the value of x? [3 marks]

Answer 1

$\angle STP={180}^{\circ }-\angle STU={180}^{\circ }-{85}^{\circ }={95}^{\circ }$ [Linear pair] [1 mark]
We have, sum of all interior angles of "n" sided polygon
$=(n-2)\times {180}^{\circ }$
$=(5-2)\times {180}^{\circ }$
$=3\times {180}^{\circ }={540}^{\circ }$
$\Rightarrow x+{90}^{\circ }+{125}^{\circ }+{130}^{\circ }+{95}^{\circ }={540}^{\circ }$
$\Rightarrow x+{440}^{\circ }={540}^{\circ }$
$\Rightarrow x={540}^{\circ }-{440}^{\circ }={100}^{\circ }$ [2 marks]