3 Marks Question

Question 13 Marks

Two lines l and m are perpendicular to the same line n. Are l and m perpendicular to each other? Give reason for your answer.

Answer

No, since, lines l and m are perpendicular to the line n. $\angle1=\angle2=90^\circ[\therefore\ \text{l}\perp\text{n}\ \text{and}\ \text{min}]$ It implies that these are corresponding angles. Hence, $\text{l}||\text{m}$

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Question 23 Marks

In Fig.which of the two lines are parallel and why?

Answer

$i.$ Sum of two interior angles $132^{\circ}+48^{\circ}=180^{\circ}\left[\therefore\right.$ equal to $\left.180^{\circ}\right]$
Here, we see that the sum of two interior angles on the same side of $n$ is $180^{\circ}$, then they are the parallel line.
$ii.$ The sum of two interior angles $73^{\circ}+106^{\circ}=179^{\circ} \neq 180^{\circ}$.
Here, we see that the sum of two interior angles on same side of $r$ is not equal to $180^{\circ}$, then they are not the parallel lines.

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Question 33 Marks

In Fig.$\angle1=60^\circ$ and $\angle6=120^\circ$ Show that the lines m and n are parallel.

Answer

We have, $\angle5+\angle6=180^\circ$ [linear pair Angles]
$\Rightarrow \angle5+120^\circ=180^\circ$
$\Rightarrow \angle5=180^\circ-120^\circ=60^\circ$ Now, $\angle1=\angle5$
$[\text{Each}=60^\circ]$ But, these are corresponding angles.
Therefore, the lines m and n are parallel.

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Question 43 Marks

In Fig. find the value of $x$ for which the lines l and m are parallel.

Answer

If a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary. Here, the two given lines I and m are parallel. Angles x and $44^{\circ}$, are consecutive interior angles on the same side of the transversal. Therefore, $x +$ $44^{\circ}=180^{\circ}$ Hence, $x=180^{\circ}-44^{\circ}=136^{\circ}$

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Question 53 Marks

Prove that a triangle must have atleast two acute angles.

Answer

If the triangle is an acute angled triangle, then all its three angles are acute angle. Each of these angles is less than $90^{\circ}$, so they can make three angles sum equal to $180^{\circ}$.
If a triangle is a right triangle, then one angle which is right angle will be equal to $90^{\circ}$ and the other two acute angles can make the three angles sum equal to $180^{\circ}$.

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MATHS 3 Marks Question

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