True False[1 Marks ]

Question 11 Mark

Two lines perpendicular to the same line are perpendicular to each other.

Answer

False
Explanation:The figure can be drawn as follows:

Here, $\text{l}\perp\text{n}$ and $\text{m}\perp\text{n}$ It is given that $\text{l}\perp\text{n},$ therefore, $\angle{1}=90^\circ\dots(\text{i})$ Similarly, we have $\text{m}\perp\text{n},$ therefore, $\angle{2}=90^\circ\dots(\text{ii})$ From (i) and (ii), we get: $\angle{1}=\angle{2}$ But these are the pair of corresponding angles. Theorem states: If a transversal intersects two lines in such a way that a pair of correspondung angles is equal, then the two lines are parallel. Thus, we can say that l || m.

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Question 21 Mark

If angles forming a linear pair are equal, then each of these angles is of measure 90°.

Answer

True
Solution:
Let one of the angle in the linear pair be x°. Then, other angle also becomes equal to x°.
Therefore, by the defination of linear pair, we get:
x + x = 180°
2x = 180°
$\text{x}=\frac{180^\circ}{2}$
x = 90°
Hence, if angles forming a linear pair are equal, then each of these angles is of measure 90°.

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Question 31 Mark

Angles forming a linear pair are supplementary.

Answer

True
Solution:
As the sum of the angles forming a linear pair is 180°.

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Question 41 Mark

If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

Answer

False
Explanation: Theoram states: If a transversal intersects two parallel lines then the pair of alternate interior angles is equal.

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Question 51 Mark

Angles forming a linear pair can both be acute angles.

Answer

False
Solution:
Let us assume one of the angle in a linear pair be x;
Such that x° < 90°, that is, an acute angle.
Therefore, the other angle in the linear pair becomes (180 - x)°, which clearly cannot be acute.

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Question 61 Mark

If two parallel lines are intersected by a transversal, then alternate interior angles are equal.

Answer

True
Explanation:
Let l and m are two parallel lines. And transversal t intersects l and m making two pair of alternate interior angles, $\angle{1},\angle{2}$ and $\angle{3},\angle{4}.$