Question

If three angles a quadrilateral are ${100}^{\circ }$,${90}^{\circ }$ and ${60}^{\circ }$, then the fourth angle will be ________.

• A. ${100}^{\circ }$
• B. ${120}^{\circ }$
• C. ${150}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

The correct option is D ${110}^{\circ }$

Sum of all angles of a quadrilateral are ${360}^{\circ }$.
Let the fourth angle be $x^{\circ }$

${100}^{\circ }+{60}^{\circ }+{90}^{\circ }+x^{\circ }={360}^{\circ }$
${250}^{\circ }+x^{\circ }={360}^{\circ }$
$x^{\circ }={360}^{\circ }-{250}^{\circ }$
$x={110}^{\circ }$