Question

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

Answer 1

Given: Angles of a quadrilateral are in AP with common difference = 10°.

Let the required angles be a, (a + 10°), (a + 20°) and (a + 30°).

Then, a + (a + 10°) + (a + 20°) + (a + 30°) = 360° 

⇒ 4a + 60°= 360° 

⇒ a = 75°

So, other angles are

a + 10° = 75° + 10° = 85°

a + 20° = 75° + 20° = 95°

a + 30° = 75° + 30° = 105°

So, Angles of a quadrilateral are 75°, 85°, 95° and 105°.

Answer 2

Sum of angles of a quadrilateral = 360°

Common difference = 10 = d (say)

If the first number be a, then the next four numbers will be

a, a + 10, a + 20, a + 30

As per definition:

a + a + 10 + a + 20 + a + 30 = 360°

4a + 60 = 360

4a = 300

or a = 75°

Other angles:

a + 10 = 75 + 10 = 85

a + 20 = 75 + 20 = 95

a + 30 = 75 + 30 = 105

Therefore, Angles are 75°, 85°, 95°, 105°