Question

The three angles of a quadrilateral are ${54}^{\circ },{76}^{\circ }$ and ${108}^{\circ }$. Find the value of fourth angle.

• A. ${116}^{\circ }$
• B. ${118}^{\circ }$
• C. ${120}^{\circ }$
• D. ${122}^{\circ }$

Answer 1

The correct option is D ${122}^{\circ }$

We know that, sum of the angles of a quadrilateral is ${360}^{\circ }$.
Let the fourth angle be $x$.
Therefore,
${54}^{\circ }+{76}^{\circ }+{108}^{\circ }+x={360}^{\circ }$
$\Rightarrow {238}^{\circ }+x={360}^{\circ }$
$\Rightarrow x={360}^{\circ }-{238}^{\circ }$
$\Rightarrow x={122}^{\circ }$

So, the measure of fourth angle $={122}^{\circ }$