Question

The sum of the two angles of a quadrilateral is 150° and the other two angles are equal. Find
the two equal angles of a quadrilateral.​

Answer 1

Answer:

The equal angles are 105° each.

Step-by-step explanation:

Given :

• The sum of the two angles of a quadrilateral is 150°
• The other two angles are equal.

To find :

the two equal angles of a quadrilateral

Solution :

Let a , b , c , d are the angles of the quadrilateral.

➙ The sum of the two angles of the quadrilateral is 150°

a + b = 150°

➙ The other two angles of the quadrilateral are equal.

c = d

In a quadrilateral, the sum of the four interior angles is 360°

a + b + c + d = 360°

150° + c + c = 360°

150° + 2c = 360°

 2c = 360° - 150°

 2c = 210°

  c = 210°/2

  c = 105°

∴ The equal angles are 105° each.

Verification :

a + b + c + d = 360°

150° + 105° + 105° = 360°

150° + 210° = 360°

   360° = 360°

   LHS = RHS

Hence verified!