A friendly flat-vector scene of labelled angle rays and a protractor in IllumiTutor navy and amber on a warm off-white background.

P4 Measuring and Drawing Angles

Put the vertex in the middle of the name, read the correct protractor scale, and construct a given angle.

⏱ 6 min · 🎯 3 things to master

An angle is the opening between two rays that share a point. That shared point is the vertex. In P4 you name angles, measure them in degrees and draw a requested size carefully.

Parents: ask your child to point to the vertex before reading a scale. A protractor has two number scales, so the baseline's 0° mark decides which numbers to read.

By the end you will be able to name an angle with the vertex in the middle, read a protractor in degrees and draw a given angle with a ruler and protractor.

Name the vertex first

In ∠ABC, the middle letter B is the vertex. The rays are BA and BC, so the name follows the route from one endpoint through B to the other endpoint. A small angle can also be named ∠a when a lower-case letter is written inside it.

🤔 Predict first: In ∠ABC, which point is the vertex?

Read the notation

∠ABC has vertex B\angle ABC\text{ has vertex }B
∠a is named by the small letter a\angle a\text{ is named by the small letter }a

Measure with the correct scale

Place the protractor's centre on the vertex and put its straight baseline on one ray. Start with the scale whose 0° mark lies on that ray. Follow that scale to the other ray and read the number in degrees. The same two rays can show 35° on one scale and 145° on the other; the baseline tells you which reading belongs to the angle.

Protractor lab: choose the matching scale

Predict first: The baseline ray points right and the target is 35°. Which reading is correct?

Text alternative: the lab shows vertex V, baseline VA and target VC. With VA pointing right, a 35° ray ends at the 35° mark on the right-zero scale; a 145° ray ends at the 145° mark on that same scale. With the baseline pointing left and the target direction at 145° from the right, choose the left-zero scale and read 35°.

Two readings on the instrument

35∘+145∘=180∘ on the semicircle scales35^{\circ}+145^{\circ}=180^{\circ}\text{ on the semicircle scales}
∠AVC=35∘ when the right-zero scale reaches C\angle AVC=35^{\circ}\text{ when the right-zero scale reaches }C
∠AVC=145∘ when the right-zero scale reaches C\angle AVC=145^{\circ}\text{ when the right-zero scale reaches }C

Draw a given angle

Use this complete ruler-and-protractor routine for a 60° angle at B.

  1. Draw the first ray from B with a ruler and label an endpoint A.
  2. Put the protractor's centre exactly on B and its baseline exactly along BA.
  3. Use the scale whose 0° mark is on BA, then mark 60°.
  4. Remove the protractor and use the ruler to draw the second ray through B and the mark; label its endpoint C.
  5. Write ∠ABC so B is the middle letter, then check that the opening is 60°.

🤔 Predict first: When drawing 60° at B, what must happen before you mark 60°?

Practise with worked steps

Practice givens 1: Rays BA and BC share vertex B. Name the angle using three letters.

Reveal solution: Practice 1

The rays are BA and BC and their shared point is B. A valid three-letter name is ∠ABC (or ∠CBA if the same two rays are used).

Name the vertex

∠ABC has middle letter B, so vertex=B\angle ABC\text{ has middle letter }B\text{, so vertex}=B

Practice givens 2: Vertex V, baseline ray VA points right, and target ray VC is 35° above VA. Find ∠AVC.

Reveal solution: Practice 2

The baseline ray points right, the target ray is 35° above it, and the vertex is V. Use the right-zero scale: ∠AVC = 35°.

Practice 2

∠AVC=35∘\angle AVC=35^{\circ}

Practice givens 3: Vertex B, first ray BA points right, and a requested angle of 60°. Draw the second ray BC and name the angle.

Reveal solution: Practice 3

Given vertex B and first ray BA, centre the protractor at B, line up the right-zero 0° mark with BA, mark 60°, remove the instrument and draw BC through the mark. The completed name is ∠ABC = 60°.

Practice 3

∠ABC=60∘\angle ABC=60^{\circ}

Watch out

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

  1. In ∠PQR, which point is the vertex?

  2. An angle is labelled ∠a. What does a name?

  3. The baseline points right and the other ray reaches 35°. Which reading is correct?

  4. The baseline points right and the target reaches 145°. Which reading is correct?

  5. Where should the protractor centre go when drawing an angle at B?

  6. Which order draws a 60° angle correctly?