CBSE Class 6 Mathematics Lines and Angles Practice Paper Worksheet Set 03 with Answers

Here is CBSE Class 6 Mathematics Ganita Prakash Chapter 2 Lines and Angles Practice Paper 06: 20 questions for 40 marks across Sections A to E, each followed by a clear step-by-step solution. The questions cover naming the vertex and arms of an angle, counting the angles formed by rays from one point, reading the inner scale of a protractor, angles on a straight line and around a point, a reflex angle on a clock face, and the angle between the hands at 2:00 and 2:30.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. Name the six angles in the given diagram that have C as a vertex.

Answer:
Four rays start from C: CD, CM, CN and CB.
Each pair of these rays makes one angle at C.
Angles between neighbouring rays: ∠DCM, ∠MCN, ∠NCB.
Angles that skip one ray: ∠DCN, ∠MCB.
Angle between the outermost rays: ∠DCB.
That is 3 + 2 + 1 = 6 angles.
In simple words: Pair up the four rays in every possible way to get six angles.

Teacher's Note:
1. List the angles in an order so none is missed.
2. Four rays from a point give 3 + 2 + 1 = 6 angles.

Question 12. Three rays originate from a point forming three angles. If two of the angles measure 85° and 95°, find the third angle. Also state whether it is acute, right, obtuse, or straight.
Answer:
The three angles go all the way round the point, so they add up to 360°.
Sum of the known angles = 85° + 95° = 180°.
Third angle = 360° − 180° = 180°.
An angle of 180° is a straight angle: two of the rays lie on one straight line.
In simple words: The third angle is 180°, a straight angle.

Teacher's Note:
1. Angles around a point add up to 360°.
2. 180° means the two arms form a straight line.

Question 13. Two adjacent angles on a straight line are in the ratio 3:2. Find their measures.
Answer:
Angles on a straight line add up to 180°.
Ratio 3 : 2 means the 180° is split into 3 + 2 = 5 equal parts.
One part = 180° ÷ 5 = 36°.
The angles are 3 × 36° = 108° and 2 × 36° = 72°.
Check: 108° + 72° = 180°.
In simple words: Split 180° into 5 equal parts of 36°: the angles are 108° and 72°.

Teacher's Note:
1. Add the ratio numbers to get the number of parts.
2. Check that the two angles total 180°.

Question 14. The hands of a clock show 9 O’clock. Find the angle between the hands. Is it acute, right, obtuse, or straight?
Answer:
At 9 o’clock the minute hand is at 12 and the hour hand is at 9.
Going the short way, from 9 to 12 there are 3 hour gaps: 3 × 30° = 90°.
So it is a right angle.
In simple words: At 9:00 the hands are a quarter turn apart: 90°, a right angle.

Teacher's Note:
1. Each hour gap is 30°.
2. 3:00 and 9:00 both show right angles.

Section C: Short Answer Questions (3 Marks Each)

Question 15. In the figure name the following angles:
(a) an acute angle at B   (b) an acute angle at E   (c) a right angle
(d) three obtuse angles   (e) a straight angle
Answer:
(a) At B, ∠ABE is the marked right angle, so the remaining part ∠CBE is acute: ∠CBE.
(b) At E, ∠AEB is less than 90°: ∠AEB (or ∠BEA).
(c) The marked angle ∠ABE = 90°.
(d) ∠ABC (= ∠ABE + ∠EBC, more than 90°), ∠BCD and ∠BED are obtuse.
(e) A, E and D lie on one line, so ∠AED is a straight angle (180°).
In simple words: ∠CBE and ∠AEB are acute, ∠ABE is right, ∠ABC, ∠BCD and ∠BED are obtuse, and ∠AED is straight.

Teacher's Note:
1. Use the right-angle mark as a reference.
2. Points on one straight line give a straight angle.

Question 16. Using the inner (anticlockwise) scale of the protractor in the below figure, find the measures of
(1) ∠a, (2) ∠b, (3) ∠c, (4) ∠d, (5) ∠ABD, (6) ∠CBE.

Answer:
On the inner scale, ray BA is at 0°, BC at 50°, BD at 100°, BE at 140° and the left part of the base line at 180°.
(1) ∠a = 180° − 140° = 40°
(2) ∠b = 140° − 100° = 40°
(3) ∠c = 100° − 50° = 50°
(4) ∠d = 50° − 0° = 50°
(5) ∠ABD = 100° − 0° = 100°
(6) ∠CBE = 140° − 50° = 90° (= ∠b + ∠c)
Check: ∠a + ∠b + ∠c + ∠d = 40° + 40° + 50° + 50° = 180°, a straight angle.
In simple words: Subtract the two scale readings of the arms to get each angle.

Teacher's Note:
1. An angle equals the difference between the readings of its arms.
2. The four small angles must add up to 180°.

Question 17. A straight angle is divided into two angles such that one angle is 40° more than the other. Find the two angles.
Answer:
The two angles together make a straight angle, 180°.
Take away the extra 40° first: 180° − 40° = 140°. This is shared equally, so the smaller angle = 140° ÷ 2 = 70°.
The larger angle = 70° + 40° = 110°.
Check: 70° + 110° = 180°, and 110° − 70° = 40°.
In simple words: The two angles are 70° and 110°.

Teacher's Note:
1. Remove the difference first, then halve.
2. Always check both conditions.

Section D: Long Answer Question (5 Marks)

Question 18. A student is playing with a protractor. He places the center of the protractor on the vertex of an angle.
(a) The student measures an angle of 150°. What type of angle is this? What is the difference between this angle and a straight angle?
(b) The student then measures an angle of 30°. What type of angle is this? What is the sum of the 150° and 30° angles?
(c) If the student wants to create an angle of 22.5°, what fraction of a right angle would this be? Show your calculation.
Answer:
(a) 150° is more than 90° and less than 180°, so it is an obtuse angle. Difference from a straight angle = 180° − 150° = 30°.
(b) 30° is less than 90°, so it is an acute angle. Sum = 150° + 30° = 180°, a straight angle; placed side by side, the two angles make a straight line.
(c) A right angle measures 90°. Fraction = \( \frac{22.5}{90} \) = \( \frac{225}{900} \) = \( \frac{1}{4} \).
Check: \( \frac{1}{4} \) × 90° = 90° ÷ 4 = 22.5°. So 22.5° is one-quarter of a right angle (half of 45°).
In simple words: 150° is obtuse (30° short of 180°), 30° is acute, together they make 180°, and 22.5° is a quarter of a right angle.

Teacher's Note:
1. Compare with 90° and 180° to classify.
2. Halving 90° twice gives 22.5°.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1: In a bustling city park, three friends, Alice, Ben, and Chloe, were discussing their afternoon plans. They were standing at a central intersection where three paved walking paths met. Alice pointed to the paths, noting the angles they formed. "Look," she said, "the path to the cafe and the one to the playground form a 120° angle. And the path to the playground and the one to the rose garden form a 95° angle."
(a) Find the measure of the third angle.
(b) What is the type of the third angle?
(c) What is the sum of the three angles?
(d) Why is it important that these three paths meet such that their angles add up to this sum?
Answer:
(a) The three angles between the paths go all the way round the meeting point, so they add up to 360°. Third angle (between the rose garden path and the cafe path) = 360° − (120° + 95°) = 360° − 215° = 145°.
(b) 145° is between 90° and 180°, so it is an obtuse angle.
(c) 120° + 95° + 145° = 360°.
(d) The three paths start from one point and together cover every direction around it, one complete turn. So their angles must add up to 360°; no gap is left and nothing overlaps. This also lets us find any one angle when the other two are known.
In simple words: The third angle is 145° (obtuse), and the three angles make one full turn of 360°.

Teacher's Note:
1. Angles around a point make a full turn.
2. Name which two paths make the third angle.

Question 20. Case Study 2: While staring at the old grandfather clock in Grandma's study, Leo waited for her to finish a phone call. The steady ticking was the only sound in the room. Leo noticed the time was exactly 2 O'clock and the hands formed a sharp, acute angle. It was the perfect moment to sneak out and grab a cookie.
(a) Find the measure of this angle.
(b) What type of angle is it?
(c) How will the angle change if the time is 2:30?
(d) Why do clock hands form different types of angles during the day?
Answer:
(a) Each hour gap is 360° ÷ 12 = 30°. At 2:00 the hands are 2 gaps apart: 2 × 30° = 60°.
(b) 60° is less than 90°, so it is an acute angle.
(c) At 2:30 the minute hand points at 6. The hour hand has moved halfway from 2 to 3, that is, half of 30° = 15° past the 2.
From the 2 to the 6 is 4 gaps = 120°, so the angle between the hands = 120° − 15° = 105°. The angle grows from 60° (acute) to 105°, which is obtuse.

(d) The two hands turn at different speeds (the minute hand goes round once every hour, the hour hand once in 12 hours), so the opening between them keeps changing. That is why the hands show zero, acute, right, obtuse, straight and reflex angles at different times of the day.
In simple words: At 2:00 the angle is 60° (acute); at 2:30 it opens to 105° (obtuse) because the hands move at different speeds.

Teacher's Note:
1. Remember that the hour hand also moves during the half hour.
2. Each minute the hour hand turns half a degree.