Question

The four angles of a quadrilateral are 3:4:8: 9
find the angles

Answer 1

Given :

• Ratio of angles of a quadrilateral are 3:4:8:9

To find :

• The angles

According to the question,

As we know,

That the sum of interior angle of a quadrilateral is 360°

So,

Let the ratio be 3x,4x,8x and 9x

→ Sum of all the ratio = Sum of interior angles of a quadrilateral

→ 3x + 4x + 8x + 9x = 360°

→ 24x = 360°

→ x = 360° ÷ 24

.°. x = 15°

So,the angles are :-

3x = 3 × 15° = 45°

4x = 4 × 15° = 60°

8x = 8 × 15° = 120°

9x = 9 × 15° = 135°

____________....

⋆ Verification :-

→ 3x + 4x + 8x + 9x = 360°

Putting the value of x = 15°

→ 3 × 15° + 4 × 15° + 8 × 15° + 9 × 15° = 360°

→ 45° + 60° + 120° + 135° = 360°

→ 360° = 360°

.°. L.H.S = R.H.S

Hence,Verified...

Answer 2

Answer:

The angels are 45°, 60°, 120°, 135°

Step-by-step explanation:

Let, the angles of a quadrilateral :

• 3x
• 4x
• 8x
• 9x

We know that,

Sum of angles of quadrilateral is 360°

So,

⇒ 3x + 4x + 8x + 9x = 360

⇒ 24x = 360

⇒ x = 360 / 24

⇒ x = 15

___________________________

★ Value of 3x :

⇒ 3 (15)

⇒ 3 × 15

⇒ 45

___________________________

★ Value of 4x :

⇒ 4 (15)

⇒ 4 × 15

⇒ 60

___________________________

★ Value of 8x :

⇒ 8 (15)

⇒ 8 × 15

⇒ 120

___________________________

★ Value of 9x :

⇒ 9 (15)

⇒ 9 × 15

⇒ 135

Therefore,

The angels are 45°, 60°, 120°, 135°