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3 years ago

Quadrilateral ABCD is inscribed in circle Pas shown. Which statement is necessarily true?

Mathematics

1 answer:

Svetradugi [14.3K]3 years ago

5 0

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.

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