Question

If the angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4, then the smallest angle in the centesimal system is _____

• A. ${30}^g$
• B. ${40}^g$
• C. ${50}^g$
• D. ${60}^g$

Answer 1

The correct option is B ${40}^g$

Let the angles be $a,2a,3a,4a$
Since Sum of angles in a quadrilateral $={360}^0$
$⟹a+2a+3a+4a={360}^0$
$⟹10a={360}^0$
$⟹a={36}^0$
So, smallest angle $a={36}^0$
And in centesimal system, we know that $1^0={\left(\frac{10}{9}\right)}^g$
$⟹{36}^0={\left(\frac{10}{9}\right)}^g\times 36={40}^g$