Question

6 The sum of opposite angles of parallelogram is 150°.
Find all the angles of the parallelogram?​

Answer 1

Answer:

150° 150° 30° 30° are all the angles of this parallelogram

Answer 2

Answer :-

• Angles of the parallelogram are 75°, 75°, 105° and 105°.

Given :-

• The sum of opposite angles of parallelogram is 150°.

To Find :-

• All angles of the parallelogram.

Solution :-

Let ABCD be the parallelogram

Here

• ∠A + ∠C = 150°

Let ∠A and ∠C be x [ opposite angles of the parallelogram are equal ]

According to question :-

⇒ x + x = 150

⇒ 2x = 150

⇒ x = 150/2

⇒ x = 75°

→ ∠A = ∠C = x = 75°

Let ∠B = ∠D = y [ opposite angles of a parallelogram are equal ]

Now

⇒ ∠A + ∠B + ∠C + ∠D = 360° [ sum of all angles of a parallelogram is 360° ]

⇒ 75 + 75 + y + y = 360

⇒ 150 + 2y = 360

⇒ 2y = 360 - 150

⇒ 2y = 210

⇒ y = 210/2

⇒ y = 105°

So

• ∠B = ∠D = 105°

Hence, all angles of the parallelogram are 75°, 75°, 105° and ,105°.