Question

The four angles of a Quadrilateral are in the ratio 1 : 2 : 3 : 4 . Find all angles .​

Answer 1

Step-by-step explanation:

Given, the four angles of a quadrilateral are in the ratio 1:2:3:4

Let the angles be x,2x,3x & 4x.

∴ x+2x+3x+4x=360

⇒10x=360

∴ x=36

0

∴ angles are 36

0

,72

0

,108

0

& 144

0

.

Answer 2

Answer:

In the question, we have to find the angles of a quadrilateral that are in the ratio 1: 2: 3: 4.

Now, it is known that if the ratio is given as a : b : c : d, then the actual numbers are ax, bx, cx, dx, where x is the common factor of all the numbers.

So, now the angles that are in ratio of 1: 2: 3: 4, can be written as x, 2x, 3x and 4x in degrees.

Here the angles are in clockwise order. The figure can be as follows:

Now, it is very well known that the sum of all the interior angles of the quadrilateral is 360 degrees.

So, the angles x, 2x, 3x and 4x in degrees are add as follows:

⇒x+2x+3x+4x=360∘⇒10x=360∘⇒x=36∘

So here the angles will be x=36∘

, 2x=72∘

, 3x=108∘

, and 4x=144∘

.

Step-by-step explanation: