An angle and a protractor

An angle is a turn

An open door. Scissors. Clock hands. A skateboarder who does a “360”. Everywhere there is an angle — a measure of a turn.

An angle is made between two arms (half-lines) that start from one point — the vertex. The more the arms are opened, the bigger the angle.

Angles are measured in degrees, mark °. A whole turn around is 360°. Why 360? The old Babylonians split the circle that way — and the number caught on, because it divides so nicely: half a turn is 180°, a quarter 90°.

A quarter turn — 90° — is the most important angle in the world: a notebook corner, a door corner, a screen corner. It is called a right angle.

For measuring angles you use a protractor — a see-through half-circle ruler with a scale from 0° to 180°. Today you will learn to handle it. It is a tool like a ruler: once you get where to put it, you measure anything.

Adam is building a ramp for an RC car and Sofie advises: “Too steep. Give it about thirty degrees.” Adam looks at her: “And how much is thirty degrees?” Sofie pulls a protractor from her pencil case: “A notebook corner is ninety. A third of a corner — like this.” She puts the protractor on the board: centre on the edge, zero along the ground, and reads on the scale: 42°. “See, you have over forty there. Prop it lower.” Adam levels the board to 30° and the car lands on its wheels for the first time. An angle is not science — it is just a number for slant.

How to measure with a protractor, step by step

A protractor has a centre mark (a small cross or a hole in the middle of the straight edge) and two scales — one from the left, the other from the right. Measuring method:

Step 1: Centre on the vertex. Put the protractor’s centre mark exactly on the vertex of the angle (the point where the arms meet).

Step 2: Zero on an arm. Turn the protractor so one arm of the angle goes through zero on the scale. The straight edge of the protractor lies along the arm.

Step 3: Read where the second arm crosses the scale. And here watch the two scales: read the one that starts at zero on your first arm. When you are not sure, the estimate decides: an angle smaller than a right angle → a number under 90.

Drawing an angle (for example 60°) is the same method backwards: draw an arm, put the protractor centre on its end point, zero on the arm, make a dot at 60° and join it to the vertex.

Write-up: angles are marked with Greek letters (α — alpha, β — beta) or three points: angle AVB, where V is the vertex (always written in the middle).

A short arm on paper does not mean a small angle! An angle is a measure of opening, not the length of the lines — you can happily lengthen the arms with a ruler, the value does not change.

Measure the angle between the arms

On paper there is an angle — two lines from one point. Method:

1. Protractor centre on the vertex (the cross exactly on the point).
2. Zero of the right-hand scale on the bottom arm.
3. The top arm crosses the scale at the numbers 50 and 130 (two scales!).

Which reading holds? Estimate: the angle is smaller than a notebook corner (90°). So 50°.

The number 130 is from the other scale — that one measures from the opposite end. An estimate first = no mix-ups.

Draw an angle of 75°

1. With a ruler draw a horizontal arm and at its left end make point V — the vertex.

2. Put the protractor: centre on V, zero along the arm.

3. On the scale (the one that starts at zero on your arm!) find 75 and make a dot by it.

4. Take the protractor off and join V to the dot with a ruler.

An estimate check: 75° is almost a right angle, just a bit closed. If your drawing looks almost like a notebook corner — it fits.

A clock as a protractor

How many degrees do the hands make at 3:00?

The clock face is a whole circle = 360°. Between twelve numbers there is 360 : 12 = 30° for one hour.

At 3:00 the small hand is on three, the big one on twelve — between them there are 3 hour ticks: 3 × 30 = 90°. A right angle! That is why people say “hands at a right angle”.

At 6:00 it is 6 × 30 = 180° — the hands in one straight line. A clock is a protractor you wear on the wall.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Mulai with ten. When it goes well, add more.

What kind of angle is it? Acute, right, obtuse, or straight?

Practise the questions

On paper

You need a protractor and a ruler. If there is no protractor at home, at least estimate from a notebook corner.

1. Draw any three angles “by hand” — small, medium, big. First estimate the degrees of each, then measure with a protractor. Compare the estimate with the measurement.

2. Draw exactly the angles 30°, 90° and 120° by the method from the lesson.

3. Find five angles at home (an open book, scissors, a chair back, a toy roof, an open door) and measure them. Write a table: thing — estimate — measured.

4. How many degrees do the clock hands make at 1:00, at 4:00 and at 6:00? Count through 30° per hour.

Now you 💪

1. I can point to the vertex and the arms of an angle and I know that the length of the arms has no effect on the size of the angle.
2. I can put a protractor correctly: centre on the vertex, zero on an arm.
3. Before reading the scale I estimate whether the angle is under or over 90°.

What to take from this lesson

• An angle = a measure of a turn between two arms with a shared vertex.
• A whole turn 360°, a half 180°, a quarter (right angle) 90°.
• Measuring: centre on the vertex, zero on an arm, read the right scale.
• An estimate before measuring (more/less than 90°?) protects you from reading the wrong scale.
• The size of an angle does not depend on the length of the arms — only on the opening.

© 2026 Ing. Martin Polak / AlgoRhino · Ketentuan penggunaan konten