Question

Three angles of a quadrilateral are ${60}^{\circ },{110}^{\circ }$ and ${86}^{\circ }$, the fourth angle of the quadrilateral is :

• A. ${104}^{\circ }$
• B. ${124}^{\circ }$
• C. ${94}^{\circ }$
• D. ${84}^{\circ }$

Answer 1

The correct option is A ${104}^{\circ }$

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

The given angles are, ${60}^o,{110}^o,{86}^o$.

Let the fourth angle be $x^o$.

Then, ${60}^o+{110}^o+{86}^o+x^o={360}^o$.

$\Rightarrow$ ${360}^o-({60}^o+{110}^o+{86}^o)=x^{\circ }$

$\Rightarrow$ $x^o={360}^o-{256}^o={104}^{\circ }$.

Therefore, the fourth angle is $x^o={104}^o$.

Hence, option $A$ is correct.