Question

If the angles of a quadrilateral are in AP and the ratio of smallest and biggest angle is 1:3. Find the angles of the quadrilateral.

Answer 1

Answer: The angles of the quadrilateral would be 45, 75, 105, and 135 degree.

Step-by-step explanation:

As the angles of a quadrilateral are in AP, the angle would be in the form given by:

a-3d, a-d, a+d, a+3d

We know that the sum of angles of the quadrilateral is 360 degree.

So,

a-3d + a-d + a+d + a+3d= 360

4a= 360

a= 90 degree

Given that the ratio of smallest and biggest angle is 1:3.

So,

(a-3d)/(a+3d)=1/3 or

(90-3d)/(90+3d)=1/3

After cross multiplying, we get:

3(90-3d)= 1(90+3d)

270-9d= 90+3d

12d= 180

d= 15

So,

The first angle of the quadrilateral= 90-3x15=45

The second angle= 90-15=75

The third angle= 90+15= 105

The fourth angle= 90 +3x15= 135

Answer 2

I hope this will help you