Question

Three angles of a quadrilateral are ${75}^{\circ },{90}^{\circ }$ and ${75}^{\circ }$. The measure of fourth angle is?

• A. ${90}^{\circ }$
• B. ${95}^{\circ }$
• C. ${105}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is D ${120}^{\circ }$

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

The given angles are, ${75}^o,{90}^o,{75}^o$.

Let the fourth angle be $x^o$.
Then, ${75}^o+{90}^o+{75}^o+x^o={360}^o$.

$\Rightarrow$ ${360}^o-({75}^o+{90}^o+{75}^o)=x^{\circ }$

$\Rightarrow$ $x^o={360}^o-{240}^o={120}^{\circ }$.

Therefore, the fourth angle is $x^o={120}^o$.

Hence, option $D$ is correct.