2 Mark Question

Question 12 Marks

For what value of x will the lines l and m be parallel to each other?

Answer

Lines l and m will be parallel if 3x - 20 = 2x + 10
[Since, if corresponding angles are equal, lines are parallel]
⇒ 3x - 2x = 10 + 20
⇒ x = 30

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Question 22 Marks

Define the following terms:
Reflex angle.

Answer

An angle greater than 180º but less than 360º is called a reflex angle.

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Question 32 Marks

In the figure given below, state which lines are parallel and why?

Answer

In the given figure,$\angle\text{BAC}=\angle\text{ACD}=110^\circ$
But, these are alternate angles when transversal AC cuts AB and CD. Hence, AB || CD.

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Question 42 Marks

Find the angle which is four times its complement.

Answer

Let the measure of the required angle be x.
Then, measure of its complement = (90º - x).
Therefore,
x = (90º - x)4
⇒ x = 360º - 4x
⇒ 5x = 360º
⇒ x = 72º
Hence, the measure of the required angle is 72º.

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Question 52 Marks

Define the following terms:
Supplementary angles.

Answer

Two angles are said to be supplementary if the sum of their measures is 180º.

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Question 62 Marks

Find theangle which is five times its supplement.

Answer

Let the measure of the required angle be x.
Then, measure of its supplement = (180º - x).
Therefore,
x = (180º - x)5
⇒ x = 900º - 5x
⇒ 6x = 900º
x = 150º
Hence, the measure of the required angle is 150º.

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Question 72 Marks

For what value of x will the lines l and m be parallel to each other?

Answer

⇔ 3x + 5 + 4x = 180 [Consecutive Interior Angle]
⇔ 7x = 175
⇔ x = 25

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Question 82 Marks

Define the following terms:
Obtuse angle.

Answer

An angle greater than 90º but less than 180º is called an obtuse angle.

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Question 92 Marks

Two lines AB and CD intersect at O. If $\angle\text{AOC}=50^\circ,$ find $\angle\text{AOD},\angle\text{BOD}$ and $\angle\text{BOC}.$

Answer

We know that if two lines intersect then the vertically-opposite angle are equal. Therefore,$\angle\text{AOC}=\angle\text{BOD}=50^\circ$
Let $\angle\text{AOD}=\angle\text{BOC}=\text{x}^\circ$ Also, we know that the sum of all angles around a point is 360°. Therefore,$\angle\text{AOC}+\angle\text{AOD}+\angle\text{BOD}+\angle\text{BOC}=360^\circ$
⇒ 50 + x + 50 + x = 360º ⇒ 2x = 260º ⇒ x = 130º Hence, $\angle\text{AOD}=\angle\text{BOC}=130^\circ$ Therefore, $\angle\text{AOD}=130^\circ,\angle\text{BOD}=50^\circ$ and $\angle\text{BOC}=130^\circ.$

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Question 102 Marks

Find the measure of an angle which is:
Equal to its supplement.

Answer

Let the measure of the rquired angle be xº.
Then, in case of supplementary angle:
x + x = 180º
⇒ 2x = 180º
⇒ x = 90º
Hence, measure of the angle that is equal to its supplement is 90º.

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Question 112 Marks

Two adjacent angles on a straight line are in the ratio 5 : 4. Find the measure of each of these angles.

Answer

Let the two adjacent angles be 5x and 4x, respectively.
Then,
5x + 4x = 180º
⇒ 9x = 180º
⇒ x = 20º
Hence, the two angles are 5 × 20º = 100º and 4 × 20º = 80º.

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Question 122 Marks

Define the following terms:
Interior of an angle.

Answer

The interior of an angle is the set of all points in its plane, which lie on the same side of OA as B and also on the same side of as A.

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Question 132 Marks

Find the measure of an angle which is:
Equal to its complement.

Answer

Let the measure of the required angle be xº.
Then, in case of complementary angle:
x + x = 90º
⇒ 2x = 90º
⇒ x = 45º
Hence, measure of the angle that is equal to its complement is 45º.

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Question 142 Marks

Define the following terms:
Angle.

Answer

rays OA and OB, with a common end-point O, form an angle AOB that is represented as $\angle\text{AOB}.$

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Question 152 Marks

In the adjoining figure, what value of x will make AOB a straight line?

Answer

AOB will be a straight line if
3x + 20 + 4x - 36 = 180º
⇒ 7x = 196º
⇒ x = 28º
Hence, x = 28 will make AOB a striaght line.

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Question 162 Marks

Two complementary angles are in the ratio 4 : 5. Find the angles.

Answer

Let the angles be 4x and 5x, respectively.
Then,
4x + 5x = 90
⇒ 9x = 90
⇒ x = 10º
Hence, the two angles are 4x = 4 × 10º = 40º and 5x = 5 × 10º = 50º.

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Question 172 Marks

Define the following terms:
Complementary angles.

Answer

Two angles are said to be complementry if the sum of their measures is 90º.

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Question 182 Marks

Find the measure of an angle which is 36º more than its complement.

Answer

Let the measure of the required angle be xº.
then, measure of its complement = (90 - x)º.
Therefore,
x - (90º - x) = 36º
⇒ 2x = 126º
⇒ x = 63º
Hence, the measure of the required angle is 63º.

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Question 192 Marks

In the adjoining figure, AOB is a straight line. Find the value of x.

Answer

We know that the sum of angles in a linear pair is 180º. Therefore,$\angle\text{AOC}+\angle\text{BOC}=180^\circ$
⇒ 62º + xº = 180º ⇒ xº = (180º - 62º) ⇒ x = 118º Hence, the value of x is 118º.

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