05 – Rule 4

Opposite angles in cyclic quadrilateral add up to 180°:

A cyclic quadrilateral has four sides with each corner touching the inside circumference of a circle.

Prove that the opposite angles in a cyclic quadrilateral add up to 180°.

i.e. Angle m + n = 180°

Draw a line from to the centre O from the left and right corner of the shape

Now compare the angles at the centre to the angles at the circumference

Angle r is twice angle m and angle s is twice n. So r+s is twice m+n

s + r = 360° so m+n = 180°

Your Turn:

Find the value of x:

Enter your answer here:

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