Question

The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.

Answer 1

Step-by-step explanation:

a + a+d + a+2d + a+3d = 360 (Sum of all angles of a quadrilateral)

4a+6d =360

4a + 6(10) = 360 (d=10=given)

4a +60 = 360

4a = 360-60

4a = 300

a = 300/4

a = 75

So the angles are:-

Angle 1 (a) =75

Angle 2 (a+d) =75+10 =85

Angle 3 (a+2d) = 75+2(10)=75+20=95

Angle 4 (a+3d) = 75+3(10)=75+30=105

Thank you...

Answer 2

The angles of the quadrilateral are 75°, 85°, 95°, 105°.

Step-by-step explanation:

Given:

Here the angles of a quadrilateral are in A.P.

Also, common difference = 10°.

Let the angles of the quadrilateral be S , S+10, S+20, S+30

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

Therefore

S+S+10+S+20+S+30 = 360°

4S + 60  = 360°

4S = 360° - 60°

4S = 300°

$S=\frac{300}{4}$

S = 75°

S+10 = 75+10 = 85°

S+20 = 75+20 = 95°

S+30 = 75+30 = 105°

Therefor, the angles of the quadrilateral are 75°, 85°, 95°, 105°.