Question

An unknown variable ‘ x’, when multiplied by four consecutive numbers 3,4,5 and 6 gives the angles of the quadrilateral its value is?

Answer 1

Answer:-

• Value of x is 20.

Given :-

• An unknown variable ‘ x’, when multiplied by four consecutive numbers 3,4,5 and 6 gives the angles of the quadrilateral.

To Find :-

• Value of x.

Solution :-

Put x in the ratio

Angles are :-

• 3x
• 4x
• 5x
• 6x

As we know that

Sum of all angles of a quadrilateral is 360°.

According to question :-

⇒ 3x + 4x + 5x + 6x = 360

⇒ 7x + 5x + 6x = 360

⇒ 7x + 11x = 360

⇒ 18x = 360

⇒ x = 360/18

⇒ x = 20

• Value of x is 20.

Put the value of x in the ratio

• First angle = 3x = 3 × 20 = 60°
• Second angle = 4x = 4 × 20 = 80°
• Third angle = 5x = 5 × 20 = 100°
• Fourth angle = 6x = 6 × 20 = 120°

Verification :-

⇒60° + 80° + 100° + 120° = 360°

⇒140° + 100° + 120° = 360°

⇒240° + 120° = 360°

⇒360° = 360°

Hence, Verified !

Answer 2

Question:-

An unknown variable ‘ x’, when multiplied by four consecutive numbers 3,4,5 and 6 gives the angles of the quadrilateral its value is?

Answer:-

• The value of x is 20°

To find:-

• Value of x

Solution:-

Put x in ratio.

Angles are:-

1. 3x
2. 4x
3. 5x
4. 6x

• Sum of all angles = 360°

$\implies \: 3x + 4x + 5x + 6x = 360 \\ \\\implies \:18x = 360 \\ \\ \implies \:x = \frac{360}{18} \\ \\ \implies \:x = 20$

• The value of x is 20°

______________________

ANGLES ARE:-

• first angle = 3× 20 = 60°
• second angle = 4× 20 =80°
• third angle = 5× 20 = 100°
• fourth angle = 6×20 = 120°