# Are opposite angles in a quadrilateral always supplementary?

## Are opposite angles in a quadrilateral always supplementary?

In a cyclic quadrilateral, opposite angles are supplementary. If a pair of angles are supplementary, that means they add up to 180 degrees. So if you have any quadrilateral inscribed in a circle, you can use that to help you figure out the angle measures.

## Why are opposite angles supplementary?

When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Two angles are said to be complementary when the sum of the two angles is 90°. Two angles are said to be supplementary when the sum of the two angles is 180°.

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What should be inscribed in a circle so that its opposite angles are supplementary?

The Inscribed Quadrilateral Theorem states that a quadrilateral can be inscribed in a circle if and only if the opposite angles of the quadrilateral are supplementary.

Why do opposite angles in a cyclic quadrilateral add up to 180?

‘Opposite angles in a cyclic quadrilateral add to 180°’ (‘Cyclic quadrilateral’ just means that all four vertices are on the circumference of a circle.) Thus the two angles in ABC marked ‘u’ are equal (and similarly for v, x and y in the other triangles.)

### How much do opposite angles add up to in a quadrilateral inscribed in a circle?

The sum of the opposite angles of a quadrilateral in a circle is 180°, as long as the quadrilateral does not cross itself.

### When can a circle be inscribed in a quadrilateral?

A quadrilateral is said to be inscribed in a circle if all four vertices of the quadrilateral lie on the circle. Quadrilaterals that can be inscribed in circles are known as cyclic quadrilaterals.

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What is the opposite angles of a quadrilateral inscribed in a circle?

The opposite angles in a cyclic quadrilateral are supplementary. i.e., the sum of the opposite angles is equal to 180˚.

Can the quadrilateral below be inscribed in a circle explain?

Inscribed Quadrilateral Theorem: A quadrilateral can be inscribed in a circle if and only if the opposite angles are supplementary. If ABCD is inscribed in ⨀E, then m∠A+m∠C=180∘ and m∠B+m∠D=180∘….Vocabulary.

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