Question

If three angles of a quadrilateral are of magnitudes ${80}^{\circ },{95}^{\circ },{120}^{\circ },$ then what is the measure of the fourth angle?

• A. $80$ ${}^o$
• B. $65$ ${}^o$
• C. $75$ ${}^o$
• D. $70$ ${}^o$

Answer 1

Answer: (B)

$65$ ${}^o$

The given angles are, ${80}^{\circ },{95}^{\circ },{120}^{\circ }$.

Let the fourth angle be $x^{\circ }$

Angle sum property states that the sum of angles of a quadrilateral is ${360}^{\circ }$.

Then, ${80}^{\circ }+{95}^{\circ }+{120}^{\circ }+x^{\circ }={360}^{\circ }$

$\Rightarrow {360}^{\circ }-({80}^{\circ }+{95}^{\circ }+{120}^{\circ })=x^{\circ }$

$\Rightarrow$ $x^{\circ }={360}^{\circ }-{295}^{\circ }$

$={65}^{\circ }$

Therefore, the fourth angle is $x^{\circ }={65}^{\circ }$

Hence, option $B$ is correct.