Question

show that each angle of quadrilateral is 90°​

Answer 1

Given that,

• The given quadrilateral ABCD will be a rectangle, if its each angle is 90°

• Since, the sum of interior angles of a quadrilateral is 360°.

∴ ∠A +∠B + ∠C + ∠D = 360°

⇒ 90° + 90° + 90° + ∠D = 360°

⇒ 270° + ∠D = 360°

⇒ ∠D = 360° – 270°

⇒ ∠D = 90°

Since,

each angle of the quadrilateral is 90°.

∴The given quadrilateral is a rectangle.

Hope it helps you friend...

Answer 2

Given that,

• The given quadrilateral ABCD will be a rectangle, if its each angle is 90°
• Since, the sum of interior angles of a quadrilateral is 360°.

∴ ∠A +∠B + ∠C + ∠D = 360°

⇒ 90° + 90° + 90° + ∠D = 360°

⇒ 270° + ∠D = 360°

⇒ ∠D = 360° – 270°

⇒ ∠D = 90°

Since,

each angle of the quadrilateral is 90°.

∴The given quadrilateral is a rectangle.

Hope it helps you friend...