Question

The angles of a quadrilateral are 4x,7x,15x and 10x. find the smallest and largest angle of the quadrilateral

Answer 1

Sum of all angles of a quadrilateral is 360 degrees.
4x + 7x + 15x + 10x = 360
36x = 360
x = 10.
Smallest angle = 4x = 40 degrees.
Largest angle = 15x = 150 degrees.

Answer 2

In a quadrilateral, the angles add up to 360°.

∴ 4x + 7x + 15x + 10x = 360° [ASP of a Quadrilateral]

⇒ 36x = 360

⇒ x = 360/36

∴ x = 10

Now we substitute x in the angles given in the question.

4x° = 4(10) = 40°

7x° = 7(10) = 70°

15x° = 15(10) = 150°

10x° = 10(10) = 100°

So, here the smallest angle is 40° (4x) and the largest angle is 150° (15x)

Hope It helps!