✅ SOLUTIONS
Class 5
Chapter 3: Angles as Turns
Math Mela · NCERT Solutions
Class 5Math Mela (NCERT)Chapter 3
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🎡 Warm-up Questions
Reema's turns on the giant wheel
Solution
| Turns taken | Total | Same as |
|---|---|---|
| 2 half turns (same direction) | 1/2 + 1/2 = 1 | a full turn |
| 2 quarter turns (same direction) | 1/4 + 1/4 = 1/2 | a half turn |
| 4 quarter turns (same direction) | 4 × 1/4 = 1 | a full turn |
Everyday objects that turn — maximum possible turn (clip, hinge, tongs, scissors, file cover)
Sample Solution
| Object | Maximum turn |
|---|---|
| Clothes clip | Less than a 1/4 turn |
| Door with hinge | More than a 1/4 turn (can open wide) |
| Tongs | Less than a 1/4 turn |
| Scissors | Less than a 1/4 turn |
| File cover | More than a 1/4 turn (can open flat, close to a 1/2 turn) |
None of these usually make a half turn or a full turn — most household hinge-objects open less than that before they stop!
Straw turns: quarter (right angle), less than quarter (acute), between quarter and half (obtuse), two quarters
Solution
"Two quarter turns" together = 1/4 + 1/4 = 1/2 turn, which is called a straight angle (it looks like a straight line — 180°)!
✍️ Let Us Do (a)-(d)
(a) Paper fan — show acute and obtuse angles
Solution — Method
Open the fan less than a quarter turn to show an acute angle. Open it more than a quarter turn (but less than half) to show an obtuse angle. Two acute turns can sometimes add up to more than an acute turn — try it: 40°+40°=80°, which is still acute (less than 90°), but 50°+50°=100° which becomes OBTUSE! So two acute angles can add up to an acute, right, OR obtuse angle depending on their exact sizes.
(b) Identify angles A–H in the cardboard house picture
Solution
📎 The angles marked on the house
| Angle | Type | Reason |
|---|---|---|
| A | Obtuse | Wide angle at the roof peak — more open than a right angle |
| B | Right | Corner where the upright pillar meets the flat roof base |
| C | Acute | Narrow, pointed peak of the small triangular support |
| D | Obtuse | Wide angle between the tilted plank and the base |
| E | Acute | Sharp, narrow angle between the crossing pieces |
| F | Right | Square corner of the block |
| G | Right | Square corner of the block |
| H | Acute | Narrow peak of the small triangle |
💡 This is a visual estimation activity — after guessing, always check your answer using your own angle-measuring tool, just like the book suggests!
(c) Make a 5-sided shape with 2 right angles, 2 obtuse angles, and 1 acute angle
Solution — Method
One easy way: draw a rectangle (which already has 4 right angles) and then chop off one corner with a single slanting line. This turns 1 right angle into 2 NEW angles — one obtuse and one acute — while keeping the other 3 corners intact. Now trim one more corner slightly to turn another right angle into an obtuse one. Final shape: a 5-sided figure (pentagon) with 2 right angles, 2 obtuse angles, and 1 acute angle. ✏️ Try drawing this in your notebook — like a rectangle with one corner "cut" twice!
(d) Angles formed by gymnasts' legs
Solution — Method
Look at how wide apart the gymnast's legs are spread:
- Legs close together, small gap → Acute angle
- Legs spread in a perfect "L" shape (like a split at 90°) → Right angle
- Legs spread wide, more than a right angle → Obtuse angle
- Legs in a full split, forming a straight line → Straight angle
🤔 Let Us Think — Circle Turns
In the circles showing endpoints of 1/2, 1/4, and 1/8 turns, draw arrows to show the starting points.
Solution — Method
To find the starting point when you know the ending point and the turn size, work backwards — rotate in the OPPOSITE direction by the same amount:
- For a 1/2 turn ending point: the starting point is exactly opposite (180° back) — draw the arrow on the exact other side of the circle.
- For a 1/4 turn ending point: rotate the end point back by 90° (a quarter circle) in the reverse direction to mark the start.
- For a 1/8 turn ending point: rotate back by 45° (one eighth of the circle) to mark the start.
💡 Use your angle-measuring tool (the eighths circle you made) — place its centre on the circle's centre, line up the marked end point, and rotate backwards by the given fraction to find where the starting arrow should be drawn.
Fold a circle into 6 equal parts. What turn is half of a 1/6 turn?
Solution
Half of 1/6 = 1/6 ÷ 2 = 1/12
Half of a 1/6 turn is a 1/12 turn — because folding a 1/6 slice in half doubles the number of equal parts from 6 to 12!
🔍 Let Us Do — Guess the Angles & Turns
Q1. Guess the measure of each angle shown (8 angles on dotted grid) — acute, right, or obtuse?
Solution — Method
This is a hands-on estimation activity. For each angle drawn on the dotted grid:
1
Look at the "gap" or "opening" between the two lines at the vertex (corner point).
2
Compare it to a right angle (an "L" shape / corner of a square) — is the gap smaller (acute), the same (right), or bigger (obtuse)?
3
Place your paper angle-measuring tool at the vertex to check your guess precisely, using a combination of eighth-turn pieces if needed.
💡 Since this activity depends on YOUR own drawn angles matching the book's grid exactly, the best approach is to physically overlay your angle tool on each one in your textbook and record: acute (small gap), right (exactly like a square corner), or obtuse (wide gap, more open than a square corner).
Q2. Guess the turn made by the arrow in each circle (a-d).
Solution
📎 The four turn circles (a)-(d)
| Part | Estimated Turn | Reasoning |
|---|---|---|
| (a) | 1/4 + 1/8 = 3/8 turn(given) | Arrow rotates clockwise past the quarter mark into the green quadrant |
| (b) | ≈ 5/8 turn | Arrow points to the South-West diagonal — that's 5 eighth-turns clockwise from the top |
| (c) | ≈ 1/8 turn | Arrow is just slightly clockwise of straight-up — one eighth-turn |
| (d) | ≈ 3/4 turn | Arrow has swept most of the way around, close to three-quarters |
💡 These are estimates from the picture — always verify your own reading using the eighth-turn angle tool you made, turning it to match the picture and counting the eighths.
Q3. Measure each angle in the given shapes (a, b, c) — acute, obtuse, or right?
Solution — Method
For shape (a): angle at vertex C (where the two crossing lines meet) — look at each of the 4 angles formed; typically opposite angles are equal, and adjacent ones combine to make a straight angle (180°).
For shape (b) — a kite/quadrilateral shape: angles at D and D′ look narrow (acute), while the angle at E at the top looks wide (obtuse).
For shape (c) — an irregular quadrilateral: the angle at F′ (marked with a small square) is a right angle; angles at F and G appear acute (narrow, marked in yellow).
💡 Use your angle tool on each traced shape to confirm — this activity is designed for hands-on checking with your paper tool, not just visual guessing.
✏️ Let Us Do — Draw Angles (Q4, Q5)
Q4. Draw angles for 1/2, 1/4 (×2), 1/8, and 1/12 turns using the given lines.
Solution — Method
1
1/2 turn: from the given ray, rotate a straight line all the way to point in exactly the opposite direction (180°).
2
1/4 turn: rotate 90° from the given ray — like an "L" shape (right angle).
3
1/8 turn: rotate 45° — halfway between the ray and a right angle.
4
1/12 turn: rotate 30° — a small, narrow angle (a third of a right angle).
💡 Use your angle-measuring tool: place its centre at the marked point, line up the "0" mark with the given ray, then draw a new ray at the correct fraction mark.
Q5. Draw angles for: 1/2, 1/4, 2/4, 1/6, 4/6, 3/12, 1/2+1/4, and 1/8+1/6 turns.
Solution
| Turn | Simplify / Combine | Angle Type |
|---|---|---|
| 1/2 | = 180° | Straight angle |
| 1/4 | = 90° | Right angle |
| 2/4 | = 1/2 = 180° | Straight angle (same as 1/2!) |
| 1/6 | = 60° | Acute angle |
| 4/6 | = 2/3 = 240° | Reflex angle (more than straight) |
| 3/12 | = 1/4 = 90° | Right angle (same as 1/4!) |
| 1/2 + 1/4 | = 3/4 = 270° | Reflex angle |
| 1/8 + 1/6 | = 3/24+4/24 = 7/24 | Acute angle (less than 1/4=6/24... wait 7/24>6/24, so just over a right angle → Obtuse) |
💡 Notice: 2/4 turn = 1/2 turn, and 3/12 turn = 1/4 turn — these are equivalent fractions, just like you learned in the Fractions chapter!
🕐 Let Us Do — Clock Turns (Q6)
Guess the turn made by the minute hand; find the final position.
Solution
| Part | Given | Working | Answer |
|---|---|---|---|
| (a) | Start: 3 o'clock (pointing right). Moves 15 min | 15/60 = 1/4 turn | 1/4 turn → final: points straight down (6 o'clock position) |
| (b) | Start: 6 o'clock (pointing down). Moves 30 min | 30/60 = 1/2 turn | 1/2 turn → final: points straight up (12 o'clock position) |
| (c) | Start: 9 o'clock (pointing left). Moves 45 min | 45/60 = 3/4 turn | 3/4 turn → final: points straight down (6 o'clock position) |
| (d) | Turns 1/12 of full turn | 60 ÷ 12 = 5 | 5 minutes |
| (e) | Turns a full circle | Full turn = 60 min always | 60 minutes |
| (f) | Turns 1/6 of full turn | 60 ÷ 6 = 10 | 10 minutes |
| (g) | Turns 4/12 of full turn | 60 × 4/12 = 20 | 20 minutes |
🕐 Golden rule: The minute hand always makes a FULL turn in exactly 60 minutes, so: Minutes = (fraction of turn) × 60
🧭 Which Direction? & Fun with Turns
Creatures made a quarter turn — clockwise or anti-clockwise?
Solution
📎 Ladybug, snail, bee, and ant — before and after their quarter turn
| Creature | Before → After | Direction |
|---|---|---|
| 🐞 Ladybug | Facing left → Facing up | Clockwise |
| 🐌 Snail | Facing lower-left → Facing lower-right | Anti-clockwise |
| 🐝 Bee | Facing left → Facing up | Clockwise |
| 🐜 Ant | Facing up → Facing left | Anti-clockwise |
💡 Trick: imagine yourself as the creature. If turning the way clock-hands move gets you from the "before" to "after" picture, it's clockwise; otherwise it's anti-clockwise.
Fun with Turns Q1 — Complete the compass-direction table
Solution
| Start | Turns | Working | End Direction |
|---|---|---|---|
| North | 2 right angles, clockwise | 2×90°=180° | South |
| South | 2 right angles, anti-clockwise | 2×90°=180° | North |
| East | 4 right angles, anti-clockwise | 4×90°=360° (full circle) | East (back to start) |
| West | 4 right angles, clockwise | 4×90°=360° (full circle) | West (back to start) |
| North | 5 right angles, clockwise | 5×90°=450°=450−360°=90° | East |
| South | 3 + 1/2 + 1/2 right angles, clockwise | (3+0.5+0.5)×90°=360° | South (back to start) |
| West | four 1/2 right angles, anti-clockwise | 4×45°=180° | East (opposite of West) |
💡 Remember: 4 right angles = 360° = one full circle, which always brings you back to where you started!
Fun with Turns Q2 — Padma faces the toy shop. What does she face after a half turn clockwise? What other way could she turn to reach the same result?
Solution
A half turn (180°) always makes you face the exact opposite direction from where you started.
If Padma was facing the toy shop, after a half turn clockwise she will face whatever is directly behind her — the opposite side of the scene (e.g., the ice-cream cart / railway crossing area behind her).
Other way to reach the same place: She could take a half turn ANTI-CLOCKWISE instead! Since 180° is exactly halfway around, turning clockwise or anti-clockwise by a half turn always lands you facing the same final direction.