Question

The angles of a quadrilateral are in the ratio 2:4:6:8 Find the measure of smallest and largest anle. How many diagonals does the quadrilateral have?​

Answer 1

Step-by-step explanation:

Given Ratio of angles :-2:3:4:6

Let each angle of the quadrilateral be 2x,3x,4x and 6x.

Sum of all the angles of a quadrilateral =360

∘

∴2x+3x+4x+6x=360

∘

⇒15x=360

∘

⇒x=

15

360

⇒x=24

∘

∴ required angles are 2×24

∘

,3×24

∘

,4×24

∘

,6×24

∘

=48

∘

,72

∘

,96

∘

,144

∘

Answer 2

Step-by-step explanation:-

Let the angle of a quadrilateral be 2x,4x,6x,8x.

The sum of the angle of quadrilateral is 360°.

2x+4x+6x+8x=360°

20x=360°

x=360/20

x=18

Then,

2x=2×18=36

4x=4×18 = 72

6x=6×18= 108

8x=8×18= 144

Hence,

The greatest angle is 144(8 degree)

The smallest angle is 36(2 degree)

There are 2 diagonal in quadrilateral.

Hope it will help u.