Question

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

What is the value of x?

• A. ${100}^{\circ }$
• B. ${110}^{\circ }$
• C. ${120}^{\circ }$
• D. ${130}^{\circ }$

Answer 1

The correct option is A ${100}^{\circ }$

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