Mathematics

In the given figure x°, y°, z° and p° are exterior angles of cyclic quadrilateral ABCD, then x° + y° + z° + p° is :

  1. 180°

  2. 270°

  3. 360°

  4. 720°

In the given figure x°, y°, z° and p° are exterior angles of cyclic quadrilateral ABCD, then x° + y° + z° + p° is : Circles, Concise Mathematics Solutions ICSE Class 10.

Circles

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Answer

We know that,

The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

In cyclic quadrilateral ABCD,

∠C = x°, ∠B = p°, ∠D = y° and ∠A = z°.

∴ x° + y° + z° + p° = ∠C + ∠D + ∠A + ∠B

We know that,

Sum of angles in a cyclic quadrilateral is 360°.

∴ ∠A + ∠B + ∠C + ∠D = 360°.

Hence, Option 3 is the correct option.

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