Question

Find the value of $x$ in the given figure.

• A. ${120}^o$
• B. ${240}^o$
• C. ${40}^o$
• D. None

Answer 1

The correct option is C ${40}^o$

In the given polygon there are $5$ sides.
So, the sum of all interior angles will be ${180}^o(5-2)$ or ${540}^o$.

Let the fifth interior angle of the polygon be $y$ as shown in the figure below.

Now,
${50}^o+{80}^o+{130}^o+{40}^o+y={540}^o$
${300}^o+y={540}^o$
$y={540}^o-{300}^o$
$y={240}^o$

Now, fifth angle and $3x$ sums ${360}^o$.

So, $y+3x={360}^o$
$\Rightarrow {240}^o+3x={360}^o$
$\Rightarrow 3x={360}^o-{240}^o$
$\Rightarrow 3x={120}^o$
$\Rightarrow x=\frac{{120}^o}{3}={40}^o$

So, option $\left(c\right)$ correct.