Grade 4Mathematics

Angles

Right angles, acute, obtuse; angles around the home and school (3.2).

📖 5 min read · 3 worked examples · 8 practice questions

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The lesson

Great to see everyone! Today we're starting a new and very exciting topic in math. At the title here: 'What is an Angle?' An angle is simply the space between two lines that meet at a single point. That meeting point has a special name: the vertex. Can you say vertex? Vertex. Think of it like the corner of your exercise book or the very tip of a piece of chalk. The opening between those two lines is the angle itself. We measure how wide this opening is using a unit called degrees, written with a little circle — like this: 45°. An angle is the amount of turn between the two lines, measured from the vertex. Angles are everywhere around you! At the corner of a book or even the slope of a roof on a house. You might also see an angle when a door swings open — the space between the open door and the door frame is an angle.

They are all around us in our homes, at school, everywhere! Let's get to know each one. First up is our friend Right Angle. Angle is exactly 90 degrees — like the corner of a madarasa window or your exercise book. It makes a perfect L shape. Next is Acute Angle. Acute angles are smaller, less than 90 degrees. Think of the sharp tip of a pencil or a thin slice of matunda — that's an acute angle! Finally, meet Obtuse Angle. An obtuse angle is more than 90 degrees. Imagine an open door or taking a big stride with your leg — that's obtuse. We have three angle friends: Right (exactly 90°), Acute (less than 90°), and Obtuse (more than 90°). I'll ask someone to start.

Great job, everyone! Angles we can find right in our homes. First, the right angle. It looks like the corner of a square. Where do you see it? Think of the corner of your TV or the edge of a plate — both form a perfect right angle. Next, an acute angle. This is smaller than a right angle. Picture a chicken's beak opening, or an open book — those sharp, narrow angles are acute. Finally, the obtuse angle — wider than a right angle. Imagine a drawer pulled halfway open, or a garden hoe handle resting against the ground. Those are obtuse angles.

That we know the three types of angles, let's look around our school to find them in real life. Keep your eyes open as we explore the classroom, playground, and assembly ground! First, let's find right angles. A right angle is exactly 90 degrees — like the corner of a desk. See how the two edges meet? That's a perfect right angle. Also, where the wall meets the floor is another right angle. Angles are everywhere in our classrooms and school buildings. Think about windows, door frames, and book corners. Acute angles are smaller than a right angle. At the tip of a flagpole without the flag — that sharp point is an acute angle. Also, when you open a pair of scissors, the blades form an acute angle. Acute angles are often sharp and pointy. Can you think of other things with acute angles? Maybe the tip of a pencil or the corner of a slice of cake? Finally, obtuse angles are larger than a right angle but not as wide as a straight line. At a sloping roof — that gentle slant is an obtuse angle. Or a child leaning back on a bench — that big opening between their body and the bench is an obtuse angle. Obtuse angles look wide and spread out. Notice them in things like open doors partly closed, or the angle of a tree branch. To remember: right angles are square corners, acute angles are small and sharp, obtuse angles are wide and gentle. Let's think about more places around our school where we might find these angles.

Worked examples

The Door's Angle

First, when the door is fully closed, there is no gap — so the angle is 0 degrees. We call this 'no angle'. Watch as the door opens just a little. The angle between the door and the wall is small — it's an acute angle. Here it's 45 degrees. When the door is half open, it forms a perfect L-shape. That's a right angle — 90 degrees. Can you see the corner of the door matches the corner of the wall? Finally, when the door is wide open, the angle is bigger than 90 degrees — it's an obtuse angle. Here it's 135 degrees. Great job, everyone! You can spot these angles all around you.

The Sofa Corner

Our sofa corner. This sofa cushion has three different angles for us to identify. Watch carefully! First, look at corner A. This is where the cushion meets the seat — it forms a right angle. A right angle is exactly like the corner of a book or a square. Can you see the perfect square corner? That's a right angle. It says 'A. At corner B. This cushion is tilted diagonally — see how it's smaller than the right angle? That's an acute angle. It's like a sharp corner, smaller than a square corner. Acute angle (tilted)' — because the cushion is tilted, the angle becomes acute. Finally, look at corner C. This is the armrest leaning back. See how wide it opens? It's bigger than a right angle. That's an obtuse angle — like a wide-open door. Obtuse angle (armrest)'. In this sofa corner we found all three types: right, acute, and obtuse. You can spot angles everywhere — even at home!

The Kite

The angles hidden inside a traditional Kenyan kite. This kite is often made from newspaper and sticks – very clever, isn't it? First, see the red lines? Those are the cross sticks. Where they meet, they form a right angle – 90 degrees, just like the corner of your notebook. Next, look at the tail. That green arrow shows an acute angle – it's smaller than a right angle, sharp like the tip of your pencil. At the top and bottom edges. That's an obtuse angle – wider than a right angle, bigger than 90 degrees. Imagine opening a door wide! Think about this: in your notebook or ruler, which angle matches the kite's tail? Which one looks like the top edge? Take a moment to picture it.

Practice questions

  • First, look at the picture of a chair leg. Think about how the leg touches the floor.
  • See the half-open book. The two covers are slightly open — they form a narrow opening.
  • Finally, look at the clock showing exactly 3:00. The hour hand points to 3, and the minute hand points to 12.
  • Great job, everyone! These questions showed us that angles are all around us — from chair legs to books to clocks.
  • Look at the corner of your school exercise book. What type of angle is it?
  • Now, think about a book that is partly open, like when you're reading. At the two leaves — the pages.
  • When you open a pair of scissors to cut paper, the blades form a wide opening. This angle is bigger than a right angle but smaller than a straight angle.
  • Imagine a window that is open only a tiny crack — just a small space. The angle between the window and the wall is very small, so it's an acute angle.

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