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BECE Mathematics 2024 Paper

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Question : 12

Total: 40

In the diagram, line

P Q

is parallel to line

S T

. Find the value of the angle marked

x

$140^{\circ}$
$220^{\circ}$
$290^{\circ}$
$285^{\circ}$

Solution:

Draw a third parallel line

a^{\circ}=35^{\circ}

(Vertically opposite angles are the same)

a^{\circ}=b^{\circ}=35^{\circ}

(Alternate angles are the same)

140^{\circ}+d^{\circ}=180^{\circ}

(Sum of angles on a straight line is 180°)

d^{\circ}=180^{\circ}-140^{\circ}

d^{\circ}=40^{\circ}

c^{\circ}=d^{\circ}=40^{\circ}

(Alternate angles are the same)

b^{\circ}+c^{\circ}+x^{\circ}=360^{\circ}

(Sum of angles in a circle is 360°)

35^{\circ}+40^{\circ}+x^{\circ}=360^{\circ}

75^{\circ}+x^{\circ}=360^{\circ}

x^{\circ}=360^{\circ}-75^{\circ}

x^{\circ}=285^{\circ}

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