Question

if all angles of a quadrilateral are in the ratio 18:9:20:25 then find each angle​

Answer 1

Answer:

The angles of a quadrilateral are :

90°, 45°, 100°, 125°

Step-by-step explanation:

Let,

The angles of a quadrilateral be:

• 18x
• 9x
• 20x
• 25x

We know that,

Sum of all angels of a quadrilateral is 360°

So,

⇒ 18x + 9x + 20x + 25x = 360

⇒ 72x = 360

⇒ x = 360 / 72

⇒ x = 5

★ Value of 18x :

⇒ 18 (5)

⇒ 90

__________________________

★ Value of 9x :

⇒ 9 (5)

⇒ 45

_________________________

★ Value of 20x :

⇒ 20 (5)

⇒ 100

_________________________

★ Value of 25x :

⇒ 25 (5)

⇒ 125

_________________________

Therefore,

The angles of a quadrilateral are :

90°, 45°, 100°, 125°

Answer 2

Given :

• Angles of a quadrilateral are in the ratio 18:9:20:25

To find :

• Measure of each angle

According to the question,

Let,

The angles be 18x,9x,20,and 25x

And,

Sum of angles of a quadrilateral is 360°

Now,

→ 18x + 9x + 20x + 25x = 360°

→ 72x = 360°

→ x = 360° ÷ 72

.°. x = 5°

____________....

Value of 18x :

→ 18x

→ 18 × 5°

→ 90°

____________....

Value of 9x :

→ 9x

→ 9 × 5°

→ 45°

____________....

Value of 20x :

→ 20x

→ 20 × 5°

→ 100°

___________....

Value of 25x :

→ 29x

→ 25 × 5°

→ 125°

So,the angles are 90°,45°,100° and 125°...