Question

The angles of a quadrilateral are in the ratio 1:2:3:4. Find the measure of each angle

Answer 1

Let us consider that the smallest angle is 'x'.

According to the given ratio, the four angles are:

1. x
2. 2x
3. 3x
4. 4x

Now, for any quadrilateral, the sum of the all four angles should be equal to 360°.

So,

x + 2x + 3x + 4x = 360°

10x = 360°

x = 36°.

Thus, the four angles are:

1. x = 36°
2. 2x = 2 × 36 = 72°
3. 3x = 3 × 36 = 108°
4. 4x = 4 × 36 = 144°