Question

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

Answer 1

Let the angle of quadrilateral be 'a'

sum of angles of quadrilateral be 360°

a+(a+d)+(a+2d)+(a+3d)=360°

4a+6d=300
4a=360-6d. (d=10°)

so,
4a=300
a=75°

Now angles of quadrilateral be
a=75°
a+d=85°
a+2d=95°
a+3d=105°

Answer 2

Let the angle ∠A = x

Then,

⇒ ∠B = x + 10°

⇒ ∠C = x + 20

⇒ ∠D = x + 30.

We know that Sum of angles of a quadrilateral = 360

⇒ x + x + 10 + x + 20 + x + 30 = 360

⇒ 4x + 60 = 360

⇒ 4x = 300

⇒ x = 75.

Hence:

⇒ ∠A = 75

⇒ ∠B = 85

⇒ ∠C = 95

⇒ ∠D = 105.

Therefore, angles in a quadrilateral are : 75,85,95 and 105.

Hope this helps!