Question

Q.(1) The angles of a quadrilateral are in the ratio 1:4:6:9. Find
the measure of each of the four angles.​

Answer 1

Answer:

The measure of each angles are 18°, 72°, 108° and 162°

Step-by-step explanation:

The angles of a quadrilateral are in the ratio 1:4:6:9

Let the common multiple be x.

∴ The angles are x, 4x, 6x and 9x

Sum of the angles of a quadrilateral = 360° ....... Formula

x + 4x + 6x + 9x = 360°

20x = 360°

x = 360°/20

x = 18

Substituting x = 18, we get,

x = 18°

4x = 4 (18) = 72°

6x = 6 (18) = 108°

9x = 9 (18) = 162°

Answer 2

☆ Solution ☆

Given :-

• The angles of a quadrilateral are in the ratio 1:4:6:9.

To Find :-

• The measure of each of the four angles.

Step-by-Step-Explaination :-

Let the angles be 1x, 4x, 6x and 9x

As we know that :-

The sum of all angles of quadrilateral = 360°

So,

1x + 4x + 6x + 9x = 360°

20x = 360°

x = 360/20

x = 18°

Thus,

The measures of each angles of quadrilateral are :-

1x = 1 × 18° = 18°

4x = 4 × 18° = 72°

6x = 6 × 18° = 108°

9x = 9 × 18° = 162°

Hence,

The angles are 18°, 72°, 108° and 162°.