8 (a) The interior angle of a regular polygon with \(n\) sides is \(150^{\circ}\).
Calculate the value of \(n\).
\[
n=
\] ............................................ [2]

(b) (i) \(K, L\) and \(M\) are points on the circle.
\(K S\) is a tangent to the circle at \(K\).
\(K M\) is a diameter and
triangle \(K L M\) is isosceles.
Find the value of \(z\).
............................................ [2]

(ii) \(A T\) is a tangent to the circle at \(A\).
Find the value of \(x\).
\(x=\) ............................................ [2]

(iii)

\(F, G, H\) and \(J\) are points on the circle.
\(E F G\) is a straight line parallel to \(J H\).
Find the value of \(y\).
............................................ .. [2]

(c)

\(A, B, C\) and \(D\) are points on the circle, centre \(O\).
\(M\) is the midpoint of \(A B\) and \(N\) is the midpoint of \(C D\).
\( OM=O N \)
Explain, giving reasons, why triangle \(O A B\) is congruent to triangle \(O C D\).
................................................................................................................................................. .
................................................................................................................................................. .
................................................................................................................................................. .
................................................................................................................................................. [3]

$$\(A T\)$$ is a tangent to the circle at $$\(A\)$$. Find the value of $$\(x\)$$. $$\(x=\)$$ ............................................

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