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JAMB Mathematics 2023 Paper

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Question : 72

Total: 80

PQRS is a cyclic quadrilateral. Find $x$ + $y$

50
60
15
0

Solution:

Concept:

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

180^\circ

.

Explanation:

For

\angle PQR

and

\angle PSR

:

(5x - y + 10) + (-2x + 3y + 145) = 180

Simplify:

3x + 2y + 155 = 180 \Rightarrow 3x + 2y = 25 \quad (1)

For

\angle QPS

and

\angle QRS

:

(-4x - 7y + 150) + (2x + 8y + 105) = 180

Simplify:

-2x + y + 255 = 180 \Rightarrow -2x + y = -75

Thus:

y = 2x - 75

Substitute into equation

(1)

:

3x + 2(2x - 75) = 25

3x + 4x - 150 = 25 \Rightarrow 7x = 175 \Rightarrow x = 25

Then:

y = 2(25) - 75 = -25

Hence:

x + y = 25 + (-25) = 0

Answer:

x + y = 0

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