Question

four angle of a quadrilateral
of angle?
are in the ratio 1:2:
34. What
is the measure each​

Answer 1

CORRECT QUESTION :-

• Find four angles of a Quadrilateral when angles are in ratio 1:2:3:4.

GIVEN :-

• Angles of Quadrilateral are in ratio 1:2:3:4.

TO FIND :-

• All angles.

SOLUTION :-

The four angles are in ratio. So, there must be a common multiple. Let that multiple be 'x'.

Angles are x , 2x , 3x and 4x respectively.

By Angle sum property , sum of all interior angles of a Quadrilateral is 360°.

→ x + 2x + 3x + 4x = 360

→ 10x = 360

→ x = 360/10

→ x = 36

Angles are :-

• x = 36°
• 2x = 2(36) = 72°
• 3x = 3(36) = 108°
• 4x = 4(36) = 144°

Angles of quadrilateral are 36° , 72° , 108° and 144°.

VERIFICATION :-

Sum of all the angles must be 360°.

36° + 72° + 108° + 144° = 360°

360° = 360° (verified)

MORE TO KNOW :-

• Sum of all interior angles of Triangle is 180°.
• Sum of all interior angles of Pentagon is 540°.
• Sum of all interior angles of Hexagon is 720°.

★ 180(n-2) is the formula for Sum of all interior angles. Here , n is number of sides.

Answer 2

Appropriate question -

• Four angles of a Quadrilateral are in the ratio of 1:2:3:4. What is the measure of each angle?

Given -

• Ratio = 1:2:3:4

To find -

• The angles of the quadrilateral?

Let -

• The angles of the ratio -

1. x
2. 2x
3. 3x
4. 4x

We know that -

• Sum of angles of a Quadrilateral = 360°

So -

$\sf x + 2x + 3x + 4x = 360 ^{ \circ}$

Now -

We will solve this equation.

Solution -

$\sf x + 2x + 3x + 4x = 360 ^{ \circ} \\ \\ \\ \implies \sf 10x = 360^{ \circ} \\ \\ \\ \implies \sf x = \cancel{ \frac{360}{10} } \\ \\ \\ \implies \boxed{\sf x = 36^{ \circ}}$

∴ The measure of each angle of the quadrilateral are 36°,72°,108° & 144°.

Verification -

$\sf x + 2x + 3x + 4x = 360 ^{ \circ}$

On substituting the values -

$\implies \sf x + 2x + 3x + 4x = 360 ^{ \circ} \\ \\\\ \implies \sf 36 + 2(36) + 3(36) + 4(36) = 360 ^{ \circ} \\ \\\\ \implies \sf 36 + 72 + 108 + 144 = 360 ^{ \circ} \\\\\\ \implies \sf 360 ^{ \circ} = 360 ^{ \circ}$