Question

In a quadrilateral $ABCD$, if $\angle A={80}^{\circ },\angle B={70}^{\circ },\angle C={130}^{\circ },$ then $\angle D$ is:

• A. ${80}^{\circ }$
• B. ${70}^{\circ }$
• C. ${130}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is A ${80}^{\circ }$

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

The given angles are $\angle A={80}^o,\angle B={70}^o,\angle C={130}^o,\angle D$.

Then, $\angle A+\angle B+\angle C+\angle D={360}^o$

$⟹$ ${80}^o+{70}^o+{130}^o+\angle D={360}^o$.

$\Rightarrow$ $\angle D={360}^o-({80}^o+{70}^o+{130}^o)$

$\Rightarrow$ $\angle D={360}^o-{280}^o={80}^{\circ }$.

Therefore, the unknown angle is $\angle D={80}^o$.

Hence, option $A$ is correct.