The sum of the angles of a quadrilateral is 360º. This can be verified by drawing a diagonal and dividing the quadrilateral into two triangles. Let ABCD be a quadrilateral and AC be a diagonal in following fig.
You know that
∠ DAC + ∠ ACD + ∠ D = 180° (1)
Similarly, in ∆ ABC,
∠ CAB + ∠ ACB + ∠ B = 180° (2)
Adding (1) and (2), we get
∠ DAC + ∠ ACD + ∠ D + ∠ CAB + ∠ ACB + ∠ B = 180° + 180° = 360°
Also, ∠ DAC + ∠ CAB = ∠ A and ∠ ACD + ∠ ACB = ∠ C
So, ∠ A + ∠ D + ∠ B + ∠ C = 360°.
i.e., the sum of the angles of a quadrilateral is 360°.
Shaalaa.com | Angle Sum Property of Quadrilaterals
In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°. The angles of the triangle formed by joining the mid-points of the sides of this triangle are
If the degree measures of the angles of quadrilateral are 4x, 7x, 9x and 10x, what is the sum of the measures of the smallest angle and largest angle?
If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is