P3 Angles: Turns, Openings and Right Angles

Open a book a little, then open it wider. The two covers make different angles. An angle is the opening between two rays that share one starting point. Its size is about the turn, not how long the rays are drawn.

Parents: ask your child to make a corner with two pencils, then rotate the corner without changing its opening. Let them compare with the set-square corner before naming the result.

By the end you will be able to name the vertex and rays of an angle, recognise a right angle, and compare openings as greater or smaller than a right angle.

An angle is an opening

The shared starting point is the vertex. In the figure below, rays OA and OB share vertex O. The angle is the opening between OA and OB. A longer ray does not make a bigger angle if it points in the same direction.

Compare with a right-angle corner

A right angle looks like a square corner. Put the corner of a set square at the vertex. If both rays follow the two sides of the corner, the opening is a right angle. Turn the whole drawing and it remains a right angle.

🔬

Angle turn lab

🤔 Predict first: If a right-angle pair is rotated, is its opening still a right angle?

YesNo

The same right angle may be horizontal and vertical, rotated, or tilted on a page. The red square marker belongs at the vertex. It is the corner relationship that matters, not the page direction or the ray lengths.

Greater than or smaller than a right angle

Compare the two openings at their vertex. If the opening spreads wider than the set-square corner, it is greater than a right angle. If it fits inside the corner, it is smaller than a right angle. The ray lengths are not the test.

Three angle practice checks

Draw the opening or compare it with a set-square corner before opening each solution.

Practice 1 — name the angle

Rays OA and OB meet at O. What is the shared vertex, and what two rays form the angle?

Show the worked identification

Read the labels

$$\text{vertex}=O$$

$$\text{rays}=OA\text{ and }OB$$

The angle is the opening at O, formed by OA and OB.

Practice 2 — compare an opening

An opening fits inside the corner of a set square. Is it right, greater than right, or smaller than right?

Show the comparison

Compare with the reference

$$\text{opening fits inside the set-square corner}$$

$$\therefore\text{ smaller than a right angle}$$

It is smaller than a right angle.

Practice 3 — rotated and tilted

Three drawings each have a red square marker at the vertex. One is horizontal, one is rotated, and one is tilted. How should each be classified?

Show the classification

Use the square marker

$$\text{horizontal corner}=\text{right angle}$$

$$\text{rotated corner}=\text{right angle}$$

$$\text{tilted corner}=\text{right angle}$$

All three are right angles because each opening matches the set-square corner.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 8 — your progress is saved on this device.

1. Rays OA and OB meet at O. What is O?

   A rayThe vertexThe angle length

2. Which description names an angle?

   The opening between two raysThe longest ray on the pageThe distance to point A

3. A corner matches the corner of a set square. What is it?

   A right angleSmaller than a right angleGreater than a right angle

4. A right-angle drawing is rotated. What is its classification?

   It stays a right angleIt becomes greaterIt becomes smaller

5. An opening spreads wider than the set-square corner. What is it?

   Smaller than a right angleA right angleGreater than a right angle

6. An opening fits inside the set-square corner. What is it?

   Greater than a right angleSmaller than a right angleA straight line

7. Two rays have different lengths but the same directions as before. What happens to their angle?

   It changes because one ray is longerIt stays the same openingIt must become a right angle

8. Which tool is suitable for a P3 right-angle comparison?

   A set squareA stopwatchA measuring jug

See my score