Question

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Maths!!
Arithmetic Progression!!

The angles of a quadrilateral are in arithmetic progression. If the greatest angle is double of the smallest angle, find all the four angles.

Answer 1

Answer:

60°, 80°, 100°, 120°

Step-by-step explanation:

Since they are in AP.

Let the angles are a, a + d, a + 2d, a + 3d.

Let smallest angle = a, then greatest angle = 2a.

⇒ 2a = a + 3d

⇒ 2a - a = 3d

⇒ a = 3d

⇒ d = a/3     ----- (1)

When d = a/3:

a = a

a + d = a + a/3 = 4a/3

a + 2d = a + 2(a/3) = 5a/3

a + 3d = a + 3(a/3) = 2a

We know that Sum of angles of a quadrilateral is 360°.

⇒ a + a + d + a + 2d + a + 3d = 360°

⇒ a + 4a/3 + 5a/3 + 2a = 360

⇒ (3a + 4a + 5a + 6a) = 1080

⇒ 18a = 1080

⇒ a = 60°.

Substitute a = 60° in (1), we get

d = a/3

d = 20.

Now,

Angles are:

a = 60°

a + d = 80°

a + 2d = 100°

a + 3d = 120°

Therefore, angles are 60°, 80°, 100°, 120°

Hope it helps!