Question

The three angles of a quadrilateral are ${80}^{\circ }$,${70}^{\circ }$and${120}^{\circ }$. The fourth angle is:

• A. ${110}^{\circ }$
• B. ${100}^{\circ }$
• C. ${90}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

Answer: (C)

${90}^{\circ }$

Three angles of quadrilateral are :

${\theta }_1={80}^o$, ${\theta }_2={70}^o$, ${\theta }_3={120}^o$.

To find ${\theta }_4:$

We know, by angle sum property, total angle of quadrilateral $={360}^o$

Then, ${\theta }_1+{\theta }_2+{\theta }_3+{\theta }_4={360}^o$

$⟹$ ${80}^o+{70}^o+{120}^o+{\theta }_4={360}^o$

$⟹$ ${270}^o+{\theta }_4={360}^o$

$⟹$${\theta }_4={360}^o-{270}^o$

$\therefore {\theta }_4={90}^o$.

Therefore, the fourth angle is ${90}^o$.

Hence, option $C$ is correct.