Question

The angle of a quadrilateral are in the following ratio find the measure of
the four angles 3:5:7:9

Answer 1

Sum of the angles of quadrilateral is equal to360∘
=> 3x+5x+7x+9x=360
24x=360
x=
360
24

x=15

Hence the angles of a quadrilateral are
3x=3×15=45
5x=5×15=75
7x=7×15=105
9x=9×15=135
Answer : 45, 75, 105, 135.

Answer 2

Sum of the angles in a quadrilateral is 360°

Define x:

Ratio of the 4 angles = 3 : 5 : 7 : 9

Let x be the constant ratio

Ratio of the 4 angles = 3x : 5x : 7x : 9x

Solve x:

3x + 5x + 7x + 9x = 360

24x = 360

x = 360 ÷ 24 = 15°

Find the angles:

3x = 3(15) = 45°

5x = 5(15) = 75°

7x = 7(15) = 105°

9x = 9(15) = 135°

Answer: The angles are 45°, 75°, 105° and 135°