Question

Angles of a quadrilateral are in the ratio 1:2:3:3. Find the measure of smallest angle of the quadrilateral.

• A. ${40}^{\circ }$
• B. ${60}^{\circ }$
• C. ${120}^{\circ }$
• D. None of the above

Answer 1

The correct option is A ${40}^{\circ }$

The angles of a quadrilateral are in the ratio 1:2:3:3

Let the angles of the quadrilateral be $x,2x,3x,3x$

Sum of angles of a quadrilateral is ${360}^{\circ }$
$\Rightarrow x+2x+3x+3x={360}^{\circ }$
$\Rightarrow 9x={360}^{\circ }$
$\Rightarrow x={40}^{\circ }$

$\therefore$ The smallest angle is $x$ which is of measure ${40}^{\circ }$.