Question

In a quadrilateral the measures of 3 angles are ${70}^o,{60}^o,{90}^o$. What would be the measure of the fourth angle?

• A. ${180}^o$
• B. ${200}^o$
• C. ${100}^o$
• D. ${140}^o$

Answer 1

The correct option is D ${140}^o$

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

The given angles are, ${70}^o,{60}^o,{90}^o$.

Let the fourth angle be $x^o$.

Then, ${70}^o+{60}^o+{90}^o+x^o={360}^o$.

$\Rightarrow$ ${360}^o-({70}^o+{60}^o+{90}^o)=x^{\circ }$

$\Rightarrow$ $x^o={360}^o-{220}^o={140}^{\circ }$.

Therefore, the fourth angle is $x^o={140}^o$.

Hence, option $D$ is correct.