Question

the measures of the four angle of quadrilateral are in the ratio 3:5:7:9. find the biggest number​

Answer 1

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°

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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.