Question

11 The angles of a quadrilaterál are in the ratio
3:4:5:6. Find the largest angle of the
quadrilateral.
​

Answer 1

☆ Solution ☆

Given :-

• The angles of a quadrilaterál are in the ratio 3 : 4 : 5 : 6

To Find :-

• The largest angle of the quadrilateral.

Step-by-Step-Explaination :-

Let the ratios be 3x, 4x, 5x and 6x

As we know that :-

Sum of interior angles of quadrilateral = 360°

So,

3x + 4x + 5x + 6x = 360°

18x = 360°

x = 360/18

x = 20

Thus,

3x = 3 × 20 = 60°

4x = 4 × 20 = 80°

5x = 5 × 20 = 100°

6x = 6 × 20 = 120°

Therefore,

The angles of quadrilateral are 60°, 80°, 100° and 120°.

Hence,

The largest angle of quadrilateral is 120°.

Answer 2

Answer:

Let the angles of the quadrilateral be 3x, 4x, 5x and 6x.

We know that the sum of all the interior angles of the quadrilateral is 360°.

According to the above problem,

$3x + 4x + 5x + 6x = 360 \\ 18x = 360 \\ \boxed{x = 20}$

The required angles are :---

$→3x = 3 \times 20 = 60 °\\ →4x = 4 \times 20 = 80° \\ →5x = 5 \times 20 = 100 °\\ →6x = 6 \times 20 = 120°$

Hence, the largest angle of the quadrilateral is 120°.