Question

What is the value of $x+3y$ in the given figure?

• A. ${240}^o$
• B. ${230}^o$
• C. ${234}^o$
• D. ${158}^o$

Answer 1

The correct option is C ${234}^o$


In the given figure,
${75}^o+y+{67}^o={180}^o$
${142}^o+y={180}^o$
$y={180}^o-{142}^o$
$y={38}^o$

Now, in the figure
We know: Sum of all interior angles of polygon having 4 sides is $(4-2)\times {180}^o={360}^o$
On adding all interior angles of given quadrilateral, we get
${38}^o+x+x+{82}^o=360$
$2x+{120}^o={360}^o$
$2x={360}^o-{120}^o$
$2x={240}^o$
$x={120}^o$

Now, $x+3y={120}^o+3\times {38}^o$
$x+3y={120}^o+{114}^o$
$x+3y={234}^o$

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