Question

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

Answer 1

Answer:

If 2:3:5:8 is the ratio of angles of a quadrilateral, then its angles are 40°, 60°, 100°and 160°

Step-by-step explanation:

Given

The ratio of angles of the quadrilateral = 2:3:5:8

Let M, N, O, and P be the angles of the quadrilateral

Then if M is 2x, N is 3x, O is 5x and P is 8x

In a quadrilateral, sum of all angles is 360°

So M+N+O+P = 360

That is, 2x+3x+5x+8x= 360

18x = 360

x =360/18 = 20

Therefore

Angle M = 2x = 2*20 = 40°

Angle N = 3x = 3*20 = 60°

Angle O= 5x = 5*20 = 100°

Angle P = 8x = 8*20 = 160°

Therefore the angles of the quadrilateral are 40°,60°, 100° and 160°

Answer 2

In context to questions asked,

We have to determine the value of the angles of quardilateral

As we know that,

Sum of all interior angles of quardilateral is 360 degree

As per questions,

Let the angles of triangle is 2x, 3x, 5x and 8x.

So,

$2x + 3x + 5x + 8x = 360 \\ 18x = 360 \\ x = \frac{360}{18} \\ x = {20}^{0}$

So, value of angles will be 40 degree, 60 degree, 100 degree and 160 degree respectively.