Angles in a Quadrilateral

Transcript

Angles in a QuadrilateralWe know that Sum of angles in a triangle is 180° But, what about Quadrilateral? Let’s try to find out Consider a quadrilateral SOME We draw diagonal SM to divide it into 2 triangles In ∆ SEM Sum of angles is 180° ∠ 1 + ∠ 2 + ∠ 3 = 180° And, in ∆ SOM Sum of angles is 180° ∠ 4 + ∠ 5 + ∠ 6 = 180° Adding (1) & (2) (∠ 1 + ∠ 2 + ∠ 3) + (∠ 4 + ∠ 5 + ∠ 6) = 180° + 180° (∠ 1 + ∠ 4) + ∠ 2 + (∠ 3 + ∠ 6) + ∠ 5 = 360° ∠ S + ∠ E + ∠ M + ∠ O = 360° Thus, Sum of angles of a quadrilateral is 360°