Question

Question 26
The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is
a) ${72}^{\circ }$
b) ${144}^{\circ }$
c) ${36}^{\circ }$
d) ${18}^{\circ }$

Answer 1

Given, the angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4.
Let the angles of the given quadrilateral be $x^{\circ },2x^{\circ },3x^{\circ }$ and $4x^{\circ }$.
$\therefore x^{\circ }+2x^{\circ }+3x^{\circ }+4x^{\circ }={360}^{\circ }$ [ sum of the angles of a quadrilateral is ${360}^{\circ }$]
$\Rightarrow 10x={360}^{\circ }\Rightarrow x=\frac{{360}^{\circ }}{10}={36}^{\circ }$
Hence, the smallest angle is ${36}^{\circ }$.