3 Marks Question

Question 13 Marks

In the figure given below, if AB is parallel to CD and CD is parallel to EF, find $\angle ACE$.

Answer

Given that AB is parallel to CD and CD is parallel to EF.
$\angle E C D=180^{\circ}-130^{\circ}=50^{\circ}$
[Sum of the interior angles of same side of transversal]
$130^{\circ}+\angle E C D=180^{\circ}$
$\angle E C D=180^{\circ}-130^{\circ}=50^{\circ}$
Also, $\angle B A C=\angle A C D=70^{\circ}$ [Alternate angles]
Now, $\angle A C D=\angle E C D+\angle A C E$
$\angle A C E=\angle A C D-\angle E C D$
$\begin{array}{l}=70^{\circ}-50^{\circ} \\ =20^{\circ}\end{array}$
Therefore, $\angle A C E=20^{\circ}$.

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Question 23 Marks

Find whether the lines AB and CD are parallel or not.

Answer

$\angle C I F+\angle F I J=180^{\circ} "[$ Linear pair $]$
$\angle C I F=180^{\circ}-\angle F I J$
$=180^{\circ}-50^{\circ}=130^{\circ}$
So, $\angle ALI =\angle CIF =130^{\circ}$.
If two parallel lines are intersected by a transversal, then each pair of corresponding angles are equal. Here, $\angle ALI =\angle CIF =130^{\circ}$ are two corresponding angles.
Hence, $A B \| C D$.

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Question 33 Marks

State which lines are parallel and why.

Answer

If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.
Since $\angle E Q R=\angle P R Q=110^{\circ}$ and lines FE and PR are intersected by a transversal DC such that the pair of alternate angles is equal.
So, FE || PR.

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