The points $$\(A, B, C, D\)$$ and $$\(E\)$$ lie on the circle. $$\(P A Q\)$$ is a tangent to the circle at $$\(A\)$$ and $$\(E C=E B\)$$. Angle $$\(E C B=80^{\circ}\)$$ and angle $$\(A B E=40^{\circ}\)$$. Find the values of $$\(v, w, x, y\)$$ and $$\(z\)$$. $$\(v=\)$$ ............... . $$\(w=\)$$ ............... . $$\(x=\)$$ ............... . $$\(y=\)$$ ............... . z= ...............

Mathematics
IGCSE&ALevel
CAIE
Exam No:0580_w20_qp_42 Year:2020 Question No:8(a)

Answer:

\([v=] 40\)
\([w=] 80\)
\([x=] 40\)
\([y=] 100\)
\([z=] 60\)

Knowledge points:

E4.7.10 angles in the same segment are equal
E4.7.11 angles in opposite segments are supplementary; cyclic quadrilaterals
E4.7.12 alternate segment theorem.

Solution:

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