Question

question 5

(a) use the diagram below to prove the theorem which states: the opposite angles of a cyclic quadrilateral are supplementary. (n is the centre of the circle.)

Explanation:

Draw construction lines

Join \(N\) to \(A\) and \(N\) to \(E\). Let the reflex angle \(\angle ANE = \hat{N}_1\) and the obtuse angle \(\angle ANE = \hat{N}_2\).

Apply angle at center theorem

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Solve for opposite angles sum

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Answer:

Construction:
Draw radii \(NA\) and \(NE\). Let the obtuse angle \(\angle ANE = \hat{N}_2\) and the reflex angle \(\angle ANE = \hat{N}_1\).

Proof:

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Similarly, by joining \(NS\) and \(NI\), it can be proven that \(\hat{A} + \hat{E} = 180^\circ\).