Question

The angles of a quadrilateral are in the ratio $1:2\hspace{0.17em}:3:4$. The smallest angle is

• A. $72°$
• B. $144°$
• C. $36°$
• D. $18°$

Answer 1

The correct option is C

$36°$

Finding the angle of quadrilateral :

We know that the sum of the interior angles of a quadrilateral is equal to $360°$.

Let us assume the angles be$x,2x,3x,4x$

$$\begin{gathered} \Rightarrow x+2x+3x+4x=360 \\ \Rightarrow 10x=360 \\ \Rightarrow x=\frac{360}{10} \\ \Rightarrow x=36° \end{gathered}$$

Therefore the angles are

$$\begin{gathered} x=36° \\ 2x=2\times 36=72° \\ 3x=3\times 36=108° \\ 4x=4\times 36=144° \end{gathered}$$

So, the smallest angle is $36°$

Hence, option (C) is the correct answer .