Question

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

Options

• 180°

• 270°

• 360°

• 720°

Answer 1

In the given figure x°, y°, z and p° are exterior angles of cyclic quadrilateral ABCD, then x° + y° + z° + p° is 360°.

Explanation:

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°