Question

If the angle of a quadrilateral are in the ratio2:3:5:8 , the smallest angle is

Answer 1

SOLUTION :

Let the angles of the quadrilateral be 2x,3x,5x and 8x.

We know, sum of the angles of a quadrilateral is 360°.

Therefore, according to the question

2x + 3x + 5x + 8x = 360°

18x = 360°

x = 360/18 = 20°

Now, on substituting the value of x then the required angles are as follows :-

2x = 2×20 = 40°

3x = 3×20 = 60°

5x = 5×20 = 100°

8x = 8×20 = 160°

Hence, the smallest angle is 40°.

Answer 2

Let us assume that , the angles of quadrilateral are 2x , 3x , 5x and 8x

We know that ,

The sum of all angles of quadrilateral is 360

Thus ,

$</p><p>\sf \Rightarrow 2x + 3x + 5x + 8x = 360 \\ \\ \sf \Rightarrow </p><p>18x = 360 \\ \\ \sf \Rightarrow </p><p>x = \frac{360}{18} \\ \\ \sf \Rightarrow x = 20$

$\therefore \sf \bold{ \underline{The \: smallest \: angle \: is \: 40 \: \: }}$