Measuring/classifying angles | Year 7

01 / LEARN

The idea, step by step

An angle measures a turn

Two rays meeting at a vertex form an angle. Imagine one ray turning until it reaches the other: the amount of turn is the angle. Degrees divide a full turn into 360 equal parts. Making either ray longer does not change the turn.

An acute angle is between $0^{\circ}$ and $90^{\circ}$ . A right angle is $90^{\circ}$ ; an obtuse angle is between $90^{\circ}$ and $180^{\circ}$ . A straight angle is $180^{\circ}$ , a reflex angle is between $180^{\circ}$ and $360^{\circ}$ , and a full turn is $360^{\circ}$ .

Choose the zero before reading the scale

Put the centre mark of the protractor exactly on the vertex. Align its straight baseline with one arm. Find the zero on that arm, then follow the scale that starts there until the second arm crosses it. A protractor often prints two readings at the same tick.

Estimate first. If the angle looks smaller than a right angle, an answer such as $140^{\circ}$ is a warning that you may have used the wrong scale. To draw an angle, draw the baseline, place the protractor, mark the required degree tick and join that mark to the vertex.

A common trap

The longer-looking arm must make the larger angle.

Instead: The angle is the turn between the arms. Extending an arm changes its length, not the angle.

02 / WORKED EXAMPLES

See the thinking

Example 1

Classify a turn

A door turns through $128^{\circ}$ . What type of angle is this?

A right angle is $90^{\circ}$ and a straight angle is $180^{\circ}$ .
$90 < 128 < 180$ , so the turn is larger than a right angle but smaller than a straight angle.

An obtuse angle.

Example 2

Read the correct scale

A protractor tick has readings 42 and 138. The starting arm is aligned with the zero on the scale that reads 42 at this tick. What is the angle?

Use the scale beginning at the zero on the starting arm.
That scale reaches 42 at the second arm.
The other reading is for a baseline pointing in the opposite direction.

42^{\circ}

, an acute angle.

Check your understanding

Is $215^{\circ}$ acute, obtuse or reflex?

Show answer

Reflex.

It is larger than $180^{\circ}$ and smaller than a full turn of $360^{\circ}$ .

03 / WORKSHEET

Your turn

6 questions · 10 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Classify an angle of $74^{\circ}$ .
1 mark
Classify an angle of $180^{\circ}$ .
1 mark
Classify an angle of $302^{\circ}$ .
1 mark
A protractor shows 37 and 143 at the second arm. The starting arm is on the zero of the scale that reads 37. State the angle and explain why 143 is unsuitable.
2 marks
Draw a $65^{\circ}$ angle using a ruler and protractor. Mark its vertex.
3 marks
The smaller angle between the hands of a clock at 3:00 is a quarter-turn. Give its size and name.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Classify an angle of $74^{\circ}$ .
1 mark
$0 < 74 < 90$ .
Acute.
Classify an angle of $180^{\circ}$ .
1 mark
A half-turn is $180^{\circ}$ .
Straight.
Classify an angle of $302^{\circ}$ .
1 mark
$180 < 302 < 360$ .
Reflex.
A protractor shows 37 and 143 at the second arm. The starting arm is on the zero of the scale that reads 37. State the angle and explain why 143 is unsuitable.
2 marks
The correct scale starts at the zero on the starting arm.
Reading the other scale measures from the opposite baseline direction.
$37^{\circ}$ .
Draw a $65^{\circ}$ angle using a ruler and protractor. Mark its vertex.
3 marks
Draw a straight baseline.
Put the protractor centre at the chosen vertex and align the correct zero.
Mark $65^{\circ}$ and draw the second arm through the mark.
A constructed acute angle of $65^{\circ}$ , with the vertex labelled.
The smaller angle between the hands of a clock at 3:00 is a quarter-turn. Give its size and name.
2 marks
A full turn is $360^{\circ}$ .
$360 \div 4 = 90$ .
$90^{\circ}$ , a right angle.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Mathematics

Year 7 angle relationships, polygon properties and classification algorithms. Chapter grouping follows the approved Ascent outline.

Official curriculum source ↗

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