Question

The interior angles of a polygon having 4 sides are in the ratio 1:2:3:4. Find the measure of each angle.​

Answer 1

${\huge {\mathfrak {Answer :-}}}$

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

So, x + 2x + 3x + 4x = 360

Or, x = 360/10 = 36.

➡️ So, the angles are 36°, 72°,108° and 144°.

That's it..

Answer 2

$<h3> !!! given the ratio of the interior angles of the polygon is 1 : 2 : 3 : 4 let the angles be x, 2x, 3x and 4x Respectively. we know that the sum of interior angles of a polygon having 4 sides is 360° therefore x + 2x + 3x + 4x = 360° →10x = 360° →x = 360/10 →x = 36° hence, the interior angles of the polygon are as follows :- 1. x = 36° 2. 2x = 2 × 36 = 72° 3. 3x = 3 × 36 = 108° 4. 4x = 4 × 36 = 144° !!! </h3>$