Question

The angle of a quadrilateral are respectively ${120}^o,{73}^o,{80}^o$. Find the fourth angle.

• A. ${87}^o$
• B. ${85}^o$
• C. ${67}^o$
• D. ${57}^o$

Answer 1

The correct option is A ${87}^o$

Let the four angles be $\angle A,\angle B,\angle C$ and $\angle D$ .

Then $\angle A={120}^o,\angle B={73}^o,\angle C={80}^o$ .

We know, by angle sum property, the sum of angles of a quadrilateral is ${360}^o$.

$⟹$ $\angle A+\angle B+\angle C+\angle D={360}^o$.

Then, $\angle D$ will be given by:

$\angle D={360}^o-\angle A-\angle B-\angle C$

$\Rightarrow \angle D={360}^o-{120}^o-{73}^o-{80}^o$

$\Rightarrow \angle D=360-{273}^o$

$\Rightarrow \angle D={87}^o$.

The measure of fourth angle is ${87}^o$.

Therefore, option $A$ is correct.