Question

the angles of a quadrilateral are in A.P with d=10 find the angles
​

Answer 1

Answer:

60° , 80° , 100° and 120°

Step-by-step explanation:

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

a - 30 + a - 10 + a + 10 + a + 30 = 360

4a = 360

a = 90°

∴ a - 3d = 90 - 30 = 60°

   a - d = 90 - 10 = 80°

   a + d = 90 + 10 = 100°

   a + 3d = 90 + 30 = 120°

∴ Angles are 60° , 80° , 100° and 120°

Answer 2

The angles are $\boxed{75^\circ, 85^\circ, 95^\circ, 105^\circ}$

Step-by-step explanation:

Let the smallest angle of the quadrilateral be a

Then the angles of the quadrilateral will be , given that the angles are in AP with common difference d

$a, a+d, a+2d, a+3d$

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

Thus,

$a+(a+d)+(a+2d)+(a+3d)=360^\circ$

$\implies 4a+6d=360^\circ$

$\implies 2a+3d=180^\circ$

But given that $d=10^\circ$

Therefore,

$2a+3\times 10^\circ=180^\circ$

$\implies 2a+30^\circ=180^\circ$

$\impllies 2a=150^\circ$

$\implies a=75^\circ$

Therefore, the angles are

$75^\circ, 75^\circ+10^\circ, 75^\circ+2\times 10^\circ, 75^\circ+3\times 10^\circ$

or, $75^\circ, 85^\circ, 95^\circ, 105^\circ$

Hope this answer is helpful.

Know More:

Similar Question:

https://brainly.in/question/8271650

https://brainly.in/question/65574