Question

Cut the four interior angle of quadrilateral and find their sum

Answer 1

Solution:

Draw any Quadrilateral ABCD.

Join AC and BD.

Now, use property of triangles to prove that sum of angles of quadrilateral is 180°.

In triangle ABC

∠1 + ∠B +∠3= 180°----(1)

In triangle ADC

∠2 + ∠D +∠4=180° -----(2)

Adding (1) and (2)

∠1 + ∠B +∠3 + ∠2 + ∠D +∠4= 180°+180°

∠A +∠B +∠C +∠D= 360°

Draw a Convex quadrilateral ABCD of your choice.

Cut Interior angles A,B,C,D with the help of blade.

With the help of protractor measure these angles.

Suppose these angles are , 69°, 131°, 85°, 75°.

You will find the sum of the angles is , 69°+ 131°+ 85°+ 75°= 360°