Question

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

Answer 1

Question:-

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

Answer:-

• The angles of quadrilateral are 40°,80°,100° and 140°

To find:-

• Angles of quadrilateral

Solution:-

• Ratio = 2:4:5:7

Put x in the ratio,

• 2x
• 4x
• 5x
• 7x

As we know,

• Sum of all angles of quadrilateral = 360°

According to question,

$\large{ \tt : \implies \: \: \: \: \: \: \: 2x + 4x + 5x + 7x = 360 \degree}$

$\large{ \tt : \implies \: \: \: \: \: \: \: 18x = 360 \degree}$

$\large{ \tt : \implies \: \: \: \: \: \: \: x = \frac{360}{18 }}$

$\large{ \tt : \implies \: \: \: \: \: \: \: x = 20 \degree}$

• The value of x is 20°

Now,

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

Hence,

The angles of quadrilateral are 40°,80°,100° and 140° respectively.

Answer 2

☆ Solution ☆

Given :-

• The angles of a quadrilateral are in the ratio 2 : 4 : 5 : 7 .

To Find :-

• The angles .

Step-by-Step-Explaination :-

Let the angle be 2x, 4x, 5x, 7x

As we know that :-

The sum of all angles of a quadrilateral = 360°

So,

2x, 4x, 5x, 7x = 360°

18x = 360°

x = 360/18

x = 20°

So,

1st angle = 2x = 2 × 20 = 40°

2nd angle = 4x = 4 × 20 = 80°

3rd angle = 5x = 5 × 20 = 100°

4th angle = 7x = 7 × 20 = 140°

Hence,

The angles are 40° , 80° , 100° and 140° .