# The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral

**Solution:**

Given: The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13.

To find: All the angles of the quadrilateral.

The sum of interior angles in a quadrilateral is 360 degrees.

Let the angles of the quadrilateral be 3x, 5x, 9x, and 13x respectively.

The sum of all interior angles of a quadrilateral is 360°.

∴ 3x + 5x + 9x + 13x = 360°

30x = 360°

x = 12°

Hence, the angles are

3x = 3 × 12 = 36°

5x = 5 × 12 = 60°

9x = 9 × 12 = 108°

13x = 13 × 12 = 156°

**☛ Check: **NCERT Solutions Class 9 Maths Chapter 8

**Video Solution:**

## The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

NCERT Maths Solutions Class 9 Chapter 8 Exercise 8.1 Question 1

**Summary:**

If the angles of a quadrilateral are in the ratio 3: 5: 9: 13, then all the angles of the quadrilateral are 36°, 60°, 108° and 156°

**☛ Related Questions:**

- If the diagonals of a parallelogram are equal, then show that it is a rectangle.
- Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
- Show that the diagonals of a square are equal and bisect each other at right angles.
- Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

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