‘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.)

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

Quadrilaterals that can be inscribed in circles are known as cyclic quadrilaterals. The quadrilateral below is a cyclic quadrilateral.

Sal uses the inscribed angle theorem and some algebra to prove that opposite angles of an inscribed quadrilateral are supplementary.

Step-by-step explanation: Which property is always true for a quadrilateral inscribed in a circle. Solution : We have given that quadrilateral inscribed in a circle. Opposite angles are supplementary .

Theorem Statement: The sum of the opposite angles of a cyclic quadrilateral is 180°.

1. Given: A cyclic quadrilateral ABCD where O is the centre of a circle.
2. Construction: Join the line segment OB and OD.
3. ∠BAD + ∠BCD = 180o Similarly,
4. ∠ABC + ∠ADC = 180o

The sum of the opposite angles of cyclic quadrilateral equals 180 degrees.

OPPOSITE ANGLES OF A CYCLIC QUADRILATERAL ARE SUPPLEMENTARY PROOF

1. To prove : ∠BAD + ∠BCD = 180°, ∠ABC + ∠ADC = 180°
2. (i) ∠BAD = (1/2)∠BOD.
3. (ii) ∠BCD = (1/2) reflex ∠BOD.
4. (iii) ∠BAD + ∠BCD = (1/2)∠BOD + (1/2) reflex ∠BOD.
5. ∠BAD + ∠BCD = (1/2)(∠BOD + reflex ∠BOD)
6. ∠BAD + ∠BCD = (1/2) ⋅ (360°)

So, the sum of the interior angles of a quadrilateral is 360 degrees.

Subtract the sum of the angles from 180 degrees to get the missing angle. For example if a triangle in a quadrilateral had the angles of 30 and 50 degrees, you would have a third angle equal to 100 degrees (180 – 80 = 100).

We know that the number of sides of a hexagon is, n = 6. By the sum of exterior angles formula, Each exterior angle of a regular polygon of n sides = 360° / n. Answer: Each exterior angle of a regular hexagon = 60°.