Given:
Quadrilateral ABCD is inscribed in a circle P.
To find:
Which statement is necessarily true.
Solution:
Quadrilateral ABCD is inscribed in a circle P.
Therefore ABCD is a cyclic quadrilateral.
In cyclic quadrilateral, opposite angles form a supplementary angles.
⇒ m∠A + m∠C = 180° --------- (1)
⇒ m∠B + m∠D = 180° --------- (2)
By (1) and (2),
⇒ m∠A + m∠C = m∠B + m∠D
This statement is necessarily true for the quadrilateral ABCD in circle P.
