Question

14. The angles of a
quadrilateral are in the ratio
4:5:10:11. Find the angles of the
quadrilateral.​

Answer 1

Given :-

Ratio of the angles of a quadrilateral = 4 : 5 : 10 : 11

To Find :-

The first angle.

The second angle.

The third angle.

The fourth angle.

Analysis :-

Consider the common ratio as a variable.

Multiply each variable to each angle given.

Make an equation accordingly such that it shows the sum of the angle is equal to the sum of a quadrilateral.

Once you get the value of the variable, substitute that value in each angle.

Solution :-

Consider the common ratio as 'x'. Then the angles would be 4x, 5x, 10x and 11x.

We know that,

Sum of a quadrilateral = 360°

Making an equation,

4x + 5x + 10x + 11x = 360

30x = 360

By transposing,

x = 360/30

x = 12°

Finding the angles,

4x = 4 × 12 = 48°

5x = 5 × 12 = 60°

10x = 10 × 12 = 120°

11x = 11 × 12 = 132°

Therefore, the angles of the quadrilateral are 48°, 60°, 120° and 132°.

Answer 2

Answer:

Given :-

• The angles of a quadrilateral are in the ratio of 4:5:10:11 .

To Find :-

• What are the angles of the quadrilateral.

Solution :-

Let, the four angle be 4x, 5x, 10x and 11x.

We know that,

Sum of Quadrilateral = 360°

According to the question,

=> 4x + 5x + 10x + 11x = 360°

=> 30x = 360°

=> x = $\dfrac{\cancel{360°}}{\cancel{30}}$

==> x = 12

Hence, the required angles are,

• 4x = 4(12) = 48°
• 5x = 5(12) = 60°
• 10x = 10(12) = 120°
• 11x = 11(12) = 132°

The four angles are 48°, 60°, 120° and 132° .