RBSE Solutions Class 6 Maths Chapter 8 Basic Geometrical Concepts and Shapes Exercise 8.3

Question 1. The road from villages Ajabgarh to Gajabgarh is drawn below. Write the name of \( \angle1 \), \( \angle2 \), \( \angle3 \), \( \angle4 \).
Answer:
(i) \( \angle1 \) = Obtuse angle
(ii) \( \angle2 \) = Right angle
(iii) \( \angle3 \) = Obtuse angle
(iv) \( \angle4 \) = Reflex angle. This angle is larger than a straight angle but less than a full circle.
In simple words: Look at each angle shown in the drawing. Then, name what type of angle it is, such as acute, obtuse, right, or reflex.

🎯 Exam Tip: Remember the definitions: Acute (less than 90°), Right (exactly 90°), Obtuse (more than 90° but less than 180°), and Reflex (more than 180° but less than 360°).

Question 2. Draw the following angles in your copy arbitrarily and write their measurement with a protractor.
(i) Obtuse angle
(ii) Straight angle
(iii) Acute angle
(iv) Right angle
Answer: To draw these angles:
(i) **Obtuse angle:** Draw a ray (a line with one endpoint). Place the protractor's center on the endpoint. Mark a point at any degree between 91° and 179° (e.g., 120°). Draw a second ray from the endpoint through this mark. This angle will be an obtuse angle.
(ii) **Straight angle:** Draw a straight line segment. This line itself represents a 180° angle.
(iii) **Acute angle:** Draw a ray. Place the protractor's center on the endpoint. Mark a point at any degree between 1° and 89° (e.g., 50°). Draw a second ray from the endpoint through this mark. This angle will be an acute angle.
(iv) **Right angle:** Draw a ray. Place the protractor's center on the endpoint. Mark a point at exactly 90°. Draw a second ray from the endpoint through this mark. This angle will be a right angle, often shown with a small square symbol at the vertex. A right angle always forms a perfect 'L' shape.
In simple words: Use a ruler to draw one side of the angle. Then, use a protractor to measure and mark the second side at the correct angle. Finally, draw the second side.

🎯 Exam Tip: Always make sure the center of your protractor is exactly on the vertex (corner) of the angle and one ray aligns with the 0° mark for accurate measurement.

Question 3. Draw the following angles using protractor.
(i) 45°
(ii) 90°
(iii) 72°
(iv) 105°
(v) 134°
(vi) 180°
(vii) 20°
(viii) 21°
Answer: To draw these angles, follow the steps for using a protractor as described in Question 2, but use the specific degree values provided. For each angle, draw a baseline, align the protractor, mark the correct degree, and draw the second line to form the angle. Here are some examples of what the drawn angles would look like:

*(Note: Diagrams for (v) 134° and (vi) 180° would be similar in concept to the examples provided.)*
In simple words: For each angle listed, use your protractor to measure and draw that exact angle. Always draw a straight line first, then use the protractor to find the correct mark for the angle.

🎯 Exam Tip: When drawing angles, ensure your pencil is sharp for clear lines and precise marks. Double-check your angle measurement with the protractor before moving on.

Question 4. With the help of compass and ruler draw the following angles:
(i) 60°
(ii) 120°
(iii) 180°
(iv) 90°
(v) 45°
Answer: To draw these angles using a compass and ruler, follow these construction steps:

(i) **Drawing \( \angle60^\circ \)**
**Step 1:** Draw a line segment AB. Take point A as the center and use a suitable radius to draw an arc that cuts the line segment AB at point P.

**Step 2:** Now, with P as the center and using the *same radius* as before, draw another arc that intersects the first arc. Mark the point of intersection as Q. Connect points A and Q. The angle \( \angle QAB \) will be \( 60^\circ \). A 60-degree angle is a basic construction from which other angles can be built.


(ii) **Drawing \( \angle120^\circ \)**
**Step 1:** Continue from the steps for drawing 60°. With Q as the center and using the same radius, draw another arc that intersects the previous arc. Mark this new point of intersection as R.

**Step 2:** Join points A and R. The angle \( \angle RAB \) will be \( 120^\circ \). This angle represents two 60-degree angles next to each other.


(iii) **Drawing \( \angle180^\circ \)**
**Step 1:** Continue from the 120° construction. With R as the center and using the same radius, draw another arc that intersects the first large arc on the baseline. Mark this point as S.

**Step 2:** Join points A and S. The line segment AS, along with AB, forms a straight line. Therefore, the angle \( \angle SAB \) is \( 180^\circ \). A straight angle is essentially a straight line.


(iv) **Drawing \( \angle90^\circ \)**
**Step 1:** First, draw a line segment AB. Take point A as the center and draw a large arc that cuts AB at P. From P, with the same radius, draw an arc Q. From Q, with the same radius, draw an arc R. These mark 60° and 120° respectively.

**Step 2:** With Q as center, draw an arc above the baseline. With R as center, and the same radius, draw another arc that intersects the previous arc. Mark this intersection point as C. Join A and C. The angle \( \angle CAB \) will be \( 90^\circ \). This angle is exactly a quarter of a full circle.


(v) **Drawing \( \angle45^\circ \)**
To construct \( \angle45^\circ \), first construct a \( 90^\circ \) angle. Then, bisect the \( 90^\circ \) angle. Bisecting an angle means dividing it into two equal parts.
**Step 1:** Construct \( \angle XAY = 90^\circ \) as shown in the diagram for \( 90^\circ \) construction above. Let the arc from X intersect the \( 90^\circ \) line at B and the horizontal line at P.
**Step 2:** With P as center and a radius more than half of PB, draw an arc. With B as center and the same radius, draw another arc intersecting the previous arc. Mark this intersection point as Q. Join A to Q. The angle \( \angle QAP \) will be \( 45^\circ \). Bisecting the right angle splits it perfectly in half.

In simple words: To draw these angles with a compass, you need to follow specific steps using arcs and lines. Start with a line segment, then open your compass to a certain size, and make marks (arcs) that help you find the correct points to draw the final angle. This method is more precise than using a protractor for certain angles.

🎯 Exam Tip: Practice each construction multiple times to understand the sequence of arcs and lines. Always keep your compass radius consistent for steps that require it, and use a sharp pencil for precision.

Question 5. Observe and find out the similar figures in the following.
Answer: Upon observing the figures provided, the similar figures (angles of the same type) are matched as follows:
(i) and (D) are both acute angles (less than 90 degrees).
(ii) and (C) are both obtuse angles (greater than 90 degrees and less than 180 degrees).
(iii) and (B) are both right angles (exactly 90 degrees). A right angle forms a perfect square corner.
(iv) and (A) are both acute angles (less than 90 degrees).
(v) and (E) are both straight angles (exactly 180 degrees). A straight angle looks like a straight line.
In simple words: Look at each picture of an angle. Then, find other pictures that show the same kind of angle. For example, find all the pointy (acute) angles, all the wide (obtuse) angles, all the square (right) angles, and all the straight-line (straight) angles.

🎯 Exam Tip: To identify similar figures, classify each figure by its type first. For angles, this means determining if it's acute, right, obtuse, or straight. Then, group the figures that fall into the same category.