The sum of the four angles of a quadrilateral is 360°
If we draw a diagonal in the quadrilateral, it divides it into two triangles.
And we know the angle sum property of a triangle i.e. the sum of all the three angles of a triangle is 180°.
The sum of angles of .
The sum of angles of .
By adding both we get
Hence, the sum of the four angles of a quadrilateral is 360°.
Example
Find A and
D, if BC || AD and
B = 52° and
C = 60° in the quadrilateral ABCD.
Solution:
Given BC ∥ AD, so ∠A and ∠B are consecutive interior angles.
So A +
B = 180° (Sum of consecutive interior angles is 180°).
B = 52°
A = 180°- 52° = 128°
A +
B +
C +
D = 360° (Sum of the four angles of a quadrilateral is 360°).
C = 60°
128° + 52° + 60° + D = 360°
D = 120°
A = 128° and
D = 120°.