the measures of the four angle of quadrilateral are in the ratio 3:5:7:9. find the biggest number
Answers
Given :-
- Ratio of the four angles of quadrilateral = 3 : 5 : 7 : 9
To find :-
- The biggest angle
Knowledge Required :-
→ Formula to calculate sum of interior angles of a polygon :-
- Sum of interior angles of polygon = (2n - 4) × 90°
where,
- n = number of sides of the polygon
Solution :-
Let the four angles of quadrilateral be 3x, 5x, 7x and 9x.
- First angle = 3x
- Second angle = 5x
- Third angle = 7x
- Fourth angle = 9x
★ Quadrilateral has 4 angles, 4 sides.
Number of sides (n) = 4
→ 3x + 5x + 7x + 9x = (2n - 4) × 90°
→ 24x = ((2 × 4) - 4) × 90°
→ 24x = (8 - 4) × 90°
→ 24x = 4 × 90°
→ 24x = 360°
→ x = 360°/24
→ x = 15°
The value of x = 15°.
Substitute the value of x in the angles of quadrilateral.
→ First angle = 3x = 3 × 15° = 45°
→ Second angle = 5x = 5 × 15° = 75°
→ Third angle = 7x = 7 × 15° = 105°
→ Fourth angle = 9x = 9 × 15° = 135°
∴ The biggest angle = 135°
━━━━━━━━━━━━━━━━━━━━
Verification :-
If the sum of all the four angles of quadrilateral is equal to 360° then the values are right.
→ 45° + 75° + 105° + 135°
→ 360°
Sum of angles of quadrilateral = 360°
Hence, verified.