Question

Three angles of a quadrilateral are ${100}^{\circ }$, ${90}^{\circ }$ and ${85}^{\circ }$ .The fourth angle is

• A. ${100}^{\circ }$
• B. ${85}^{\circ }$
• C. ${65}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B

${85}^{\circ }$

Given the three angles of a quadrilateral are ${100}^{\circ }$, ${90}^{\circ }$ and ${85}^{\circ }$. Let the fourth angle be 'x'
$\because$ The sum of the angles of a quadrilateral is ${360}^{\circ }$
$\Rightarrow {100}^{\circ }+{90}^{\circ }+{85}^{\circ }+x^{\circ }={360}^{\circ }$
$\Rightarrow x={360}^{\circ }-275$
$\Rightarrow x={85}^{\circ }$

$\therefore$ The fourth angle is 85${}^{\circ }$.