THE ANGLES OF QUADRILETRAL ARE IN THE RATIO OF3:5:9:13. FIND THE DIFFERENCE BETWEEN LARGEST AND SMMALEST ANGLE. *
Answers
Given :
The angles of a quadrilateral are in the ratio 3:5:9:13
To Find :
Difference between largest and smallest angle
Concept :
First , we need to find the all angles of the quadrilateral .
After that , we get the difference
Angel sum property of a quadrilateral
This property states that the sum of all angles of a quadrilateral is 360°.
- ∠A + ∠B + ∠C + ∠D = 360°
Solution :
Let the angles of a quadrilateral be 3x , 5x , 9x and 13x
- Where x is a multiple.
↬∠A = 3x
↬∠B = 5x
↬∠C = 9x
↬∠D = 13x
According to the concept :
↬∠A + ∠B + ∠C + ∠D = 360°
↬3x + 5x + 9x + 13x = 360°
↬30x = 360°
↬x = 360° ÷ 30
↬x = 360/30
↬x = 12
↬∠A = 3x
↬∠A = 3 × 12
↬∠A = 36°
↬∠B = 5x
↬∠B = 5 × 12
↬∠B = 60°
↬∠C = 9x
↬∠C = 9 × 12
↬∠C = 108°
↬∠D = 13x
↬∠D = 13 × 12
↬∠D = 156°
Now , finding difference :
Difference between largest and smallest angle
- Largest angle = 156°
- Smallest angle = 36°
Difference = Largest angle - Smallest angle
Difference = 156° - 36°
Difference = 120°
Hence , the difference between largest and smallest angle is 120°