Question

The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8. Find the measure of each angle of the quadrilateral​

Answer 1

The angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8. Find the smallest angle of the quadrilateral

We will use the fact that the sum of angles of a quadrilateral is 360∘.

Sum of angles of quadrilateral is 360∘ ………(1)

Now, we have the ratio of angles as 2 : 3 : 5 : 8.

Let the first angle be 2x, so then according to the ratio, the angles will be 2x,3x,5x,8x.

Now using (1), we will have:-

2x+3x+5x+8x=360∘

Simplifying the LHS, we will have:-

18x=360∘

Taking the 15 from multiplication in LHS to division in RHS, we will have:-

x=360∘18=40∘2=20∘

Hence, x=20∘.

So, the angles will be 40∘,60∘,100∘,160∘.

Answer 2

Answer

Sum of angles of quadrilateral is 360∘ ………(1)

Now, we have the ratio of angles as 2 : 3 : 5 : 8.

Let the first angle be 2x, so then according to the ratio, the angles will be 2x,3x,5x,8x.

Now using (1), we will have:-

2x+3x+5x+8x=360∘

Simplifying the LHS, we will have:-

18x=360∘

Taking the 15 from multiplication in LHS to division in RHS, we will have:-

x=360∘18=40∘2=20∘

Hence, x=20∘.

So, the angles will be 40∘,60∘,100∘,160∘