Question

If three angles of a quadrlateral are ${84}^{\circ }$, ${100}^{\circ }$ and ${93}^{\circ }$, find its fourth angle.

• A. ${93}^{\circ }$
• B. ${53}^{\circ }$
• C. ${83}^{\circ }$
• D. ${63}^{\circ }$

Answer 1

The correct option is C

${83}^{\circ }$

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

$\because$ Sum of interior angles of a quadrilateral $={360}^{\circ }$.

$\Rightarrow {84}^{\circ }+{100}^{\circ }+{93}^{\circ }+x={360}^{\circ }$

$\Rightarrow x={360}^{\circ }-({84}^{\circ }+{100}^{\circ }+{93}^{\circ })$

$\Rightarrow x=({360}^{\circ }-{277}^{\circ })={83}^{\circ }$