Question

The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6, find the smallest angle.

• A. ${100}^{\circ }$
• B. ${80}^{\circ }$
• C. ${60}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is C

${60}^{\circ }$

Let the angles be $3x,4x,5x$ and $6x$.

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

$\Rightarrow 3x+4x+5x+6x={360}^{\circ }$

$\Rightarrow 18x={360}^{\circ }$

$\Rightarrow x=\frac{{360}^{\circ }}{18}$

$\Rightarrow x={20}^{\circ }$

$\therefore$ The angles are -

$3x=3\times 20={60}^{\circ }$

$4x=4\times 20={80}^{\circ }$

$5x=5\times 20={100}^{\circ }$

$6x=6\times 20={120}^{\circ }$

$\therefore$ The smallest angle is ${60}^{\circ }$.