Two lines AB and DE are parallel to each other. The line CM is parallel to both the lines AB and DE. AE and BD intersect each other at point C. If $∠$ BCM = $40^{\circ}$ and $∠$ CED = $60^{\circ}$ , find the value of $∠$ ACB and $∠$ ACD.

[3 Marks]

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Solution

$∠$ CED = $60^{\circ}$
$∠$ CED = $∠$ MCE
[ $∵$ Alternate interior angles]
So, $∠$ MCE = $60^{\circ}$ [ 1 Mark]

$∠$ BCM = $40^{\circ}$
$∠$ ACD = $∠$ BCM + $∠$ MCE [ $∵$ Vertically opposite angles]

$∠$ ACD = $40^{\circ}$ + $60^{\circ}$ = $100^{\circ}$ [1 Mark]

$∠$ ACB + $∠$ BCM + $∠$ MCE = $180^{\circ}$ [ $∵$ Angles on a straight line]

$∠$ ACB = $180^{\circ}$ - $(40^{\circ} + 60^{\circ}) = 80^{\circ}$ [ 1 Mark]

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