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WAEC Mathematics 2021 Paper

Question : 36

Total: 49

Solution:

Concept:

In a cyclic quadrilateral, the sum of each pair of opposite angles is

180^\circ

Explanation:

Using the opposite angles of cyclic quadrilateral

PQRS

, we get:

x + (x+y) = 180^\circ

So,

2x + y = 180^\circ

... (1)

Also,

x + (2y - 30^\circ) = 180^\circ

So,

x + 2y = 210^\circ

... (2)

Multiply equation (2) by

2

2x + 4y = 420^\circ

Subtract equation (1) from this result:

(2x + 4y) - (2x + y) = 420^\circ - 180^\circ

3y = 240^\circ

y = 80^\circ

Substitute

y = 80^\circ

into equation (1):

2x + 80^\circ = 180^\circ

2x = 100^\circ

x = 50^\circ

Answer:

x = 50^\circ

, which is option A.

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