2 Marks Questions

Question 12 Marks

Draw angles with the following degree measures:
(a) $140^{\circ}$
(b) $82^{\circ}$
(c) $195^{\circ}$
(d) $70^{\circ}$
(e) $35^{\circ}$

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Question 22 Marks

Use a protractor to find the measure of each angle. Then classify each angle as acute, obtuse, right, or reflex.
a. $\angle PTR$
b. $\angle PTQ$
c. $\angle PTW$
d. $\angle W T P$

Answer

(a) $\angle PTR =300$ acute
(b) $\angle PTQ =60^{\circ}$ acute
(c) $\angle PTW =105^{\circ}$ obtuse
(d) $\angle WTP =225^{\circ}$ reflex

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Question 32 Marks

Use a protractor to draw angles having the following degree measures:
(a) $110^{\circ}$
(b) $40^{\circ}$
(c) $75^{\circ}$
(d) 1120
(e) $134^{\circ}$

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Question 42 Marks

Here is a toy with slanting slabs attached to its sides; the greater the angles or slopes of the slabs, the faster the balls roll. Can angles be used to describe the slopes of the slabs?

Answer

Greater the angle, greater the slope.
For each angle one arm is a side and one arm is the slope.

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Question 52 Marks

The angle of a door: Is it possible to express the amount by which a door is opened using an angle? What will be the vertex of the angle and what will be the arms of the angle?

Answer

Yes, it is possible.

Here, vertex is B, and arms are AB and BC.

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Question 62 Marks

Get a slanting crease on the paper. Now, try to get another crease that is perpendicular to the slanting crease.
(b) Describe how you folded the paper so that any other person who doesn’t know the process can simply follow your description to get the right angle.

Answer

To create a right angle
I. First fold Start by folding the paper so that one corner meets the opposite edge, creating a slant crease.
II. Second fold Now, fold the paper again but this time align the slanting crease with the edge of the paper, ensuring the fold is perpendicular to the first crease.
III. Unfold When you open the paper, you will see that the two creases intersect at a 90° angle, forming four right angles.
Explanation The second fold must be made
carefully, aligning the first crease with the edge of the paper to insure the two creases are perpendicular. This guarantees that the angles formed are exactly 90°.

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Question 72 Marks

Get a slanting crease on the paper. Now, try to get another crease that is perpendicular to the slanting crease.
(a) How many right angles do you have now? Justify why the angles are exact right angles?

Answer

You will have four right angles now.
Explanation When you fold the paper to create a crease that is perpendicular to the first, the two creases intersect at a right angle dividing the plane into four right angles of 90° each.

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Question 82 Marks

Now, join A to other grid points in the figure by a straight line to get a right angle. What are all the different ways of doing it?

Hint: Extend the line further as shown in the figure below. To get a right angle at A, we need to draw a line through it that divides the straight angle CAB into two equal parts.

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Question 92 Marks

How many right angles do the windows of your classroom contain? Do you see other right angles in your classroom?

Answer

A window has 4 right angles.
$\angle 1, \angle 2, \angle 3$ and $\angle 4$.
Yes. At comers of door. At comers of blackboard etc.

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Question 102 Marks

Which angle is greater: $\angle X O Y$ or $\angle A O B?$ Give reasons.

Answer

On comparing by superimposition, the angles $\angle X O Y$ and $\angle A O B$ in the given figure, we get
$\angle X O Y$ is greater than $\angle A O B$ because size of $\angle X O Y$ is greater.

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Question 112 Marks

In each case, determine which angle- is greater and why.

(a) $\angle A O B$ or $\angle X O Y$
(b) $\angle A O B$ or $\angle X O B$
(c) $\angle X O B$ or $\angle X O C$
Discuss with your friends on how you decided which one is greater.

Answer

On comparing the given angles in the figure by superimposition.
(a) $\angle A O B$ is greater because size of $\angle A O B$ is greater than size of $\angle X O Y$.
(b) $\angle A O B$ is greater because size of $\angle A O B$ is greater than size of $\angle X O B$.
(c) $\angle X O B$ and $\angle X O C$ both are equal angle because vertex $O$ and one ray $\overrightarrow{O X}$ are common and $\operatorname{arm} \overrightarrow{O B}$ and $\overrightarrow{O C}$ are overlaping.

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Question 122 Marks

Now mark any four points on your paper so that no three of them are on one line. Label them A, B, C and D. Draw all possible lines going through pairs of these points. How many lines do you get? Name them. How many angles can you name using A, B, C and D? Write them all down and mark each of them with a curve as in given figure.

Answer

Point $A, B, C$ and $D$ are as follow

Possible lines are $A B, B C, C D, A D, A C$ and $B D$.
Thus, there are six lines formed and angles are
$\angle B A C, \angle B A D, \angle A D B, \angle A D C, \angle D C A, \angle D C B, \angle A B D$, $\angle A B C, \angle C A D, \angle B D C, \angle A C B$ and $\angle D B C$.
Thus, there are total twelve angles formed.

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Question 132 Marks

Mark any three points on your paper that are not on one line. Label them A, B and C. Draw all possible lines going through pairs of these points. How many lines do you get? Name them. How many angles can you name using A, B and C? Write them down and mark each of them with a curve as in given figure.

Answer

Lines are $A B, B C$ and $A C$ and formed angles are $\angle B A C$, $\angle B C A$ and $\angle C B A$.

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Question 142 Marks

Name the angles marked in the given figure.

Answer

Angles in the figure are :
Angle 1 is $\angle R T P$
Angle 2 is $\angle R T Q$

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Question 152 Marks

Explain why $\angle A P C$ cannot be labelled as $\angle P$.

Answer

In the given figure, $\overrightarrow{P B}$ divides $\angle A P C$ in two parts and makes two angles $\angle A P B$ and $\angle C P B$.
So, $\angle A P C$ is greater than $\angle A P B$ and $\angle C P B$.
Therefore, $\angle A P C$ cannot be labelled as $\angle P$.

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Question 162 Marks

Draw and label an angle with arms ST and SR.

Answer

An angle with arms $S T$ and $S R$ is $\angle T S R$.

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Question 172 Marks

Can you find the angles in the given pictures? Draw the rays forming any one of the angles and name the vertex of the angle.

Answer

Yes,

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Question 182 Marks

Puzzle: I am an acute angle. If you double my measure, you get an acute angle. If you triple my measure, you will get an acute angle again. If you quadruple (four times) my measure, you will get an acute angle yet again! But if you multiply my measure by 5, you will get an obtuse angle measure. What are the possibilities for my measure?

Answer

The possibilities for measure are $20^{\circ}$,$21^{\circ}$and $22^{\circ}$

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Question 192 Marks

In Fig. below, list all the angles possible. Did you find them all? Now, guess the measures of all the angles. Then, measure the angles with a protractor. Record all your numbers in a table. See how close your guesses are to the actual measures.

Answer

The given figure has 20 angles.
Guess: $\angle 1=\angle 4=60^{\circ} ; \angle 2=\angle 3=120^{\circ}$ by actual measure: $\angle 1=\angle 4=70^{\circ} ; \angle 2=\angle 3=110^{\circ}$.

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Question 202 Marks

Find the degree measures of $\angle B X E, \angle C X E, \angle A X B$ and $\angle E X C$.

Answer

In the given figure, on measuring each angle by placing the protractor at the vertex X and reading the angles formed by the rays, we get
$\angle B X E=115^{\circ}$, $\angle C X E=85^{\circ}$
$\angle AXB =65^{\circ}$ and $\angle BXC =30^{\circ}$

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Question 212 Marks

How can you find the degree measure of the angle given below using a protractor?

Answer

To measure the given angle
I. Place the protractor Position the centre point of the protractor at the vertex of the angle.
II. Align the baseline Align one of the angles ray with the 0° mark on the protractor's base line.
III. Measure the angle Look at where the other ray crosses the protractor's scale and read the degree measure.

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