Question

The angels of a quadrilateral are in the ratio 3:5:7:9. What is the difference between the least ans the greatest angles of the quadrilateral

Answer 1

Answer:

90°

Step-by-step explanation:

Let the numbers be x

So, it will be 3x , 5x , 7x and 9x

The Angle Sum property of quadrilateral = 360°

3x + 5x + 7x + 9x = 360°

24x = 360°

x = 360/24

x = 15°

∴ the angles are 3x = 3 × 15 = 45

                            5x = 5 × 15 = 75

                            7x = 7 × 15 = 105

                            9x = 9 × 15 = 135

∴ the angles are 45° , 75° , 105° , 135°

The greatest angle = 135°

The smallest angle = 45°

Difference between the greatest and smallest angle = 135°- 45°

                                                                                        = 90°

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