Using the angle sum property of a triangle, find the sum of the angles of any quadrilateral,
Share
Using the angle sum property of a triangle, find the sum of the angles of any quadrilateral,
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Step-by-step explanation:
Theorem and Proof of angle sum property of a quadrilateral.
Prove that the sum of all the four angles of a quadrilateral is 360°.
Proof: Let ABCD be a quadrilateral. Join AC.
Clearly, ∠1 + ∠2 = ∠A ...... (i)
And, ∠3 + ∠4 = ∠C ...... (ii)
We know that the sum of the angles of a triangle is 180°.
Angle Sum Property of a Quadrilateral
1Save
Therefore, from ∆ABC, we have
∠2 + ∠4 + ∠B = 180° (Angle sum property of triangle)
From ∆ACD, we have
∠1 + ∠3 + ∠D = 180° (Angle sum property of triangle)
Adding the angles on either side, we get;
∠2 + ∠4 + ∠B + ∠1 + ∠3 + ∠D = 360°
⇒ (∠1 + ∠2) + ∠B + (∠3 + ∠4) + ∠D = 360°
⇒ ∠A + ∠B + ∠C + ∠D = 360° [using (i) and (ii)].
Hence, the sum of all the four angles of a quadrilateral is 360°.