In the figure, radii divide the opposite angles into parts. Using the isosceles triangles formed by equal radii, we get p + v = 90° and q + u = 90°. Hence, opposite angles sum to 180°.
How would you use the following figure to justify the statement that the sum of the opposite angles of a cyclic quadrilateral is 180°?
Share
In the figure, OA, OB, OC and OD are equal radii. Therefore, the triangles formed by these radii are isosceles. Since BOD is a diameter, the angles around the centre give:
p + v = 90°
and similarly,
q + u = 90°.
Now, ∠A = p + v = 90° and ∠C = q + u = 90° in the corresponding construction, so the opposite angles together give 180°. Thus, the sum of the opposite angles of a cyclic quadrilateral is 180°.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-5/