Angles of a quadrilateral are in the ratio 3 : 4 : 4 : 7. Find all the angles of the quadrilateral.

Solution:

Given, angles of a quadrilateral are in the ratio 3 : 4 : 4 : 7

We have to find all the angles of the quadrilateral.

We know that the sum of all the angles of a quadrilateral is equal to 360 degrees.

Let the angles of the quadrilateral be 3x, 4x, 4x and 7x.

So, 3x + 4x + 4x + 7x = 360º

10x + 8x = 360º

18x = 360º

x = 360º/18

x = 60º/3

x = 20º

Now, 3x = 3(20º) = 60º

4x = 4(20º) = 80º

7x = 7(20º) = 140º

Therefore, the angles of the quadrilateral are 60º, 80º, 80º and 140º.

✦ Try This: Angles of a quadrilateral are in the ratio 3 : 5 : 6 : 7. Find all the angles of the quadrilateral.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 8

NCERT Exemplar Class 9 Maths Exercise 8.3 Sample Problem 1

Angles of a quadrilateral are in the ratio 3 : 4 : 4 : 7. Find all the angles of the quadrilateral.

Summary:

Angles of a quadrilateral are in the ratio 3 : 4 : 4 : 7. All the angles of the quadrilateral are 60º, 80º, 80º and 140º

☛ Related Questions:

• In Fig.8.3, X and Y are respectively the mid-points of the opposite sides AD and BC of a parallelogr . . . .
• In Fig.8.4, AX and CY are respectively the bisectors of the opposite angles A and C of a parallelogr . . . .
• One angle of a quadrilateral is of 108º and the remaining three angles are equal. Find each of the t . . . .