Question

Q1. The angles of a quadrilateral are in the ratio 2:4:5:7 .Find the largest angle.



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Answer 1

Step-by-step explanation:

Let the common Factor be as y

By angle sum property,

2y + 4y + 5y + 7 y = 360°

18y = 360°

y = 360

18

y = 20

.·. 7 y = 7 x 20

= 140

Answer 2

• Given

• Ratio of angles of quadrilateral = 2 : 4 : 5 : 7

• To find

• The largest angle of the quadrilateral

• Concept

• Firstly, we will let the angles given in the ratio = 2x, 4x, 5x and 7x.
• Then we will find the sum of angles of quadrilateral.
• To find each angle of quadrilateral, we will add the angles which we have let and keep them equal to the sum of angles of quadrilateral.

• Solution

Let the angles of quadrilateral be 2x, 4x, 5x and 7x.

A quadrilateral has 4 sides, 4 angles.

$\purple{\bigstar}$ $\boxed{\underline{\sf{Sum~ of ~interior~ angles = (2n - 4)90^{\circ}}}}$

where,

• n is the no. of sides.

⟶ (2 × 4) - 4 × 90°

⟶ 8 - 4 × 90°

⟶ 4 × 90°

⟶ 360°

• Sum of interior angles of quadrilateral = 360°

⟶ 2x + 4x + 5x + 7x = 360°

⟶ 18x = 360°

⟶ x = 360°/18

⟶ x = 20°

The value of x = 20°

The angles of quadrilateral -

• 2x = 2 × 20° = 40°
• 4x = 4 × 20° = 80°
• 5x = 5 × 20° = 100°
• 7x = 7 × 20° = 140°

The largest angle of quadrilateral = 140°

_____________________________________

Let's verify the angles -

The sum of angles of quadrilateral = 360°

All the angles of quadrilateral = 40°, 80°, 100°, 140°.

Their sum -

⟶ 40° + 80° + 100° + 140°

⟶ 360°

Hence, verified.