Question
Prove that the sum of all the angles of a quadrilateral is 360°.
Solution
Given: ABCD is a quadrilateral
To Prove: ∠A + ∠B + ∠C + ∠D = 360°
Construction: Join AC.
Proof: In ∆ABC,
∠1 + ∠B + ∠3 = 180° ...(1)
| Angle sum property of a triangle
In ∆ADC,
∠2 + ∠D + ∠4 = 180° ...(2)
| Angle sum property of a triangle
Adding (1) and (2), we get
(∠1 + ∠2) + ∠B + (∠3 + ∠4) + ∠D = 360°
∠ ∠A + ∠B + ∠C + ∠D = 360°
