The angles of a quadrilateral are in the ratios 2 : 4: 6 : 8. The smallest of these angles is:

Correct option is D

Given:

Ratio of angles: 2 : 4 : 6 : 8 

Concept Used: ​

Sum of all interior angle of quadrilateral is 360^o​

Solution:

Let the angles be $$2x, 4x, 6x$$ and $$8x$$.

We know that,

The sum of angles of a quadrilaterals is $$360^∘$$.

$$2x+4x+6x+8x=360^∘$$

$$20x=360^∘$$

$$x=\dfrac{360^∘}{20}$$

$$x=18^∘$$

Now, substitute the value of $$x$$ in given angles,

$$2x=2(18^∘)=36^∘$$

​​$$4x=4(18^∘)=72^∘$$

$$6x=6(18^∘)=108^∘$$

​$$8x=8(18^∘)=144^∘$$

Therefore, the smallest angle is $$36^∘$$.

Thus, the correct option is D.

​​​