Question

Three angles of a quadrilateral are ${70}^{\circ },{120}^{\circ }$ and ${65}^{\circ }$. Then the fourth angle of the quadrilateral is:

• A. ${95}^{\circ }$
• B. ${75}^{\circ }$
• C. ${105}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

Answer: (C)

${105}^{\circ }$

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

The given angles are, ${70}^o,{120}^o,{65}^o$.

Let the fourth angle be $x^o$.

Then, ${70}^o+{120}^o+{65}^o+x^o={360}^o$ ...{Angle sum property of a quadrilateral}

$\Rightarrow$ ${360}^o-({70}^o+{120}^o+{65}^o)=x^{\circ }$

$\Rightarrow$ $x^o={360}^o-{255}^o={105}^{\circ }$.

Therefore, the fourth angle is $x^o={105}^o$.

Hence, option $B$ is correct.