Question

PQRS is quadrilateral whose angle are in ratio 1: 3:7:9.find the measure of each angle. name the quadrilateral.

Answer 1

Let the ratios be x.
Then, 1 = 1x.
3 = 3x.
7 = 7x.
9 = 9x.
Sum Of Angles Of Quadrilateral = 360°.
x + 3x + 7x + 9x = 360°
20x = 360°
x = 360/20
x = 18.
3x = 3 * 18 = 54.
7x = 7 * 18 = 126.
9x = 9 * 18 = 162.
162 + 126 + 54 +18 = 360.                             Answer........................

Answer 2

Given:

Quadrilateral = PQRS

Ratio of angles =  1: 3:7:9

To Find:

The measure of each angle

Solution:

Let the ratios be = x

Therefore,

1: 3:7:9 will be -

1 = 1x, 3 = 3x, 7 = 7x, 9 = 9x.

Sum Of Angles Of the Quadrilateral = 360°

Substituting the values -

x + 3x + 7x + 9x = 360°

20x = 360°

x = 360/20

x = 18

Substituting the value of x = 18 as per the ratio -

3x  = 3 × 18

= 54.

7x = 7 × 18

= 126.

9x = 9 × 18

= 162.

Checking -

18 + 54 + 126 + 162

= 360

Answer: The measure of angles is 18, 54, 126 and 162