CBSE Class 6 Mathematics Shapes Assignment Set 06

Question. By simply looking at the pair of angles given below, state which of the angles in each pairs is greater:
(i) Angle AOB and Angle DEF
(ii) Angle GHI and Angle JKL
(iii) Angle MWN and Angle QPR
(iv) Angle SUT and Angle O
Answer:
(i) Angle AOB is greater than Angle DEF.
(ii) Angle JKL is greater than Angle GHI.
(iii) Angle MWN is greater than Angle QPR.
(iv) Angle O (complete angle) is greater than Angle SUT (straight angle).

Question. State the kind of angle given below:
(a) Angle with right angle mark (vertex O, arms OA and OB)
(b) Angle on a straight line (vertex O, arms OA and OB)
(c) Angle less than \(90^\circ\) (vertex O, arms OA and OB)
(d) Angle greater than \(90^\circ\) but less than \(180^\circ\) (vertex O, arms OA and OB)
(e) Angle with arc on the outer reflex side (vertex O, arms OA and OB)
(f) Angle with a full circular arc (vertex O, arm OA)
Answer:
(a) Right angle
(b) Straight angle
(c) Acute angle
(d) Obtuse angle
(e) Reflex angle
(f) Complete angle

Question. Using a ruler only, draw an acute, obtuse and reflex angle.
Answer:
To draw these angles using a ruler only (without a protractor), we can estimate the relative positions of the rays:
1. Acute Angle: Draw a horizontal ray. From the vertex, draw another ray that is tilted less than a vertical line (less than \(90^\circ\)).
2. Obtuse Angle: Draw a horizontal ray. From the vertex, draw another ray that is tilted further than a vertical line but not in a straight line (between \(90^\circ\) and \(180^\circ\)).
3. Reflex Angle: Draw two rays meeting at a vertex (like an acute or obtuse angle) and mark the outer angle (which is greater than \(180^\circ\) but less than \(360^\circ\)) with an arc.

Question. Convert the following angles of degrees into fractional right angle:
(a) \( 10^\circ \)
(b) \( 135^\circ \)
(c) \( 40^\circ \)
(d) \( 70^\circ \)
Answer:
(a) \( \frac{1}{9} \) right angle
(b) \( \frac{3}{2} \) right angle
(c) \( \frac{4}{9} \) right angle
(d) \( \frac{7}{9} \) right angle

Question. Convert the following into degrees:
(a) \( \frac{2}{9} \) right angle
(b) \( \frac{1}{4} \) right angle
(c) \( \frac{3}{4} \) right angle
Answer:
(a) \( 20^\circ \)
(b) \( 22\frac{1}{2}^\circ \)
(c) \( 67\frac{1}{2}^\circ \)

Question. If you are standing facing South. In which direction will you look if you turn in anti-clockwise direction through:
(a) two right angles
(b) three right angles
(c) four right angles
(d) one right angle
Answer:
(a) North
(b) West
(c) South
(d) East

Question. Name the types of following angles:
(a) less than \( 90^\circ \)
(b) equal to \( 90^\circ \)
(c) more than \( 90^\circ \) but less than \( 180^\circ \)
(d) more than \( 180^\circ \) but less than \( 360^\circ \)
Answer:
(a) Acute angle
(b) Right angle
(c) Obtuse angle
(d) Reflex angle

Question. Construct the following angles with the help of protractor:
(a) \( 45^\circ \)
(b) \( 90^\circ \)
(c) \( 30^\circ \)
(d) \( 60^\circ \)
(e) \( 120^\circ \)
(f) \( 50^\circ \)
Answer:
To construct these angles using a protractor:
1. Draw a straight ray (baseline) starting from a vertex.
2. Place the center of the protractor at the vertex and align the baseline of the protractor with your ray.
3. Locate the required degree mark on the appropriate scale (inner or outer, depending on the direction of your ray) and make a point.
4. Remove the protractor and use a ruler to draw a line from the vertex through the point.

Question. State the kind of angle formed between the following directions clock-wise:
(a) West and North
(b) West and East
(c) North and South
(d) West and South
Answer:
(a) Right angle
(b) Straight angle
(c) Straight angle
(d) Reflex angle

Question. Draw any acute angle \( \angle ABC \). Now, construct an angle \( \angle DEF \) equal to \( \angle ABC \) using a compass.
Answer:
Steps of Construction:
1. Draw any acute angle \( \angle ABC \) using a ruler.
2. Draw a ray \( EF \) which will be one arm of the new angle.
3. Place the compass point at the vertex \( B \) of the given angle \( \angle ABC \) and draw an arc of any convenient radius that intersects the arms \( AB \) and \( BC \) at points \( P \) and \( Q \), respectively.
4. Without changing the compass width, place the compass point at the vertex \( E \) of the ray \( EF \) and draw an arc that intersects \( EF \) at a point \( R \).
5. Now, place the compass point at \( Q \) and adjust its width to match the distance between \( P \) and \( Q \).
6. With this width, place the compass point at \( R \) and draw an arc intersecting the previously drawn arc at point \( S \).
7. Draw a ray \( ED \) from \( E \) passing through the intersection point \( S \).
8. The constructed angle \( \angle DEF \) is equal to the given angle \( \angle ABC \).