Question

The angles of a quadrilateral are in the ratio 2 : 5 : 6 : 5. Find the greatest and least angles.​

Answer 1

Answer:

let angles of quadrilateral be 2x 5x 6x amd 7x.

largest angle will be 7x.

u can verify it

as we know sum of all angles of a quadrilateral is 360°

so 2x+5x+6x+5x=360

18x=360

x=20

1st angle =40°

2nd angle=100°

3rd angle=120°

4th angle=100°

hence largest angle is 120°& smallest is 40°

Mark me Brainliest please,

Answer 2

Answer:-

The greatest angle = 120°

The least angle = 40°

___________________________

Given:-

The angles of a quadrilateral are in ratio 2:5:6:5.

Find the greatest and the least angles.

___________________________

Solution:-

Let the numbers given in the ratio be 2x, 5x, 6x, 5x.

We know that the sum of all angles of a quadrilateral = 360°

So,

$\tt \angle A + \angle B + \angle C + \angle D = 360°$

(Angle sum property)

2x + 5x + 6x + 5x = 360°

18x = 360°

x = $\tt \dfrac{360°}{18}$

x = 20°

.

Hence, the four angles of the quadrilateral are:

First angle:

2x = 2 x 20 = 40°

Second angle:

5x = 5 × 20 = 100°

Third angle:

6x = 6 × 20 = 120°

Fourth angle:

5x = 5 × 20 = 100°

.

So,

The greatest angle = 120°

The least angle = 40°

___________________________

Finale Answer:-

Greatest angle = 120°

Least angle = 40°