Question

In the figure given above, 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 ${100}^{\circ }$

The given figure $PQRST$ is a pentagon.

We know that, the sum of interior angles of an n-sided polygon is $(n-2){180}^o$.

$\therefore$ The sum of the internal angles of the pentagon $={540}^o$...........(i)

$\angle RQP={90}^o$ (given).

Now $\angle STP+\angle STU={180}^o$ (linear pair)

$\therefore \angle STP+{85}^o={180}^o$

$\Rightarrow \angle STP={180}^o-{85}^o$

$\Rightarrow \angle STP={95}^o$

Again, the sum if the internal angles of $PQRST$

$=x+{90}^o+{130}^o+{95}^o+{125}^o$

$={x+440}^o={540}^o$ [From (i)]

$\Rightarrow x={100}^o$.

Hence, the value of $x$ is ${100}^o$.