Measuring/classifying angles | Year 7

01 / LEARN

Understand the idea.

An angle measures a turn

An angle measures the turn between two rays meeting at a vertex. One full turn is $360^{\circ}$ . Extending an arm changes its length but leaves the angle unchanged because the direction of each ray stays the same.

Acute angles lie between $0^{\circ}$ and $90^{\circ}$ ; obtuse angles lie between $90^{\circ}$ and $180^{\circ}$ ; reflex angles lie between $180^{\circ}$ and $360^{\circ}$ . The boundary cases have their own names: right $90^{\circ}$ , straight $180^{\circ}$ , and full turn $360^{\circ}$ .

Choose the zero before reading the scale

Place the protractor centre on the vertex and its baseline along one arm. Find the zero at that starting arm, then follow that same scale to the second arm. The other printed scale measures from the opposite end.

Estimate the angle type before reading. An apparently acute angle should give a reading below $90^{\circ}$ . To draw an angle, mark the required tick from the correct zero, then draw a ray from the vertex through that mark.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Classify a turn

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

Worked solution

1
Locate the nearest angle boundaries.
$90^{\circ} < 128^{\circ} < 180^{\circ}$
The turn exceeds a right angle but is less than a straight angle.
2
Apply the classification.
Any angle strictly between 90 degrees and 180 degrees is obtuse, so this door turn is obtuse.

Answer

An obtuse angle.

EXAMPLE 02

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?

Worked solution

1
Choose the scale starting at the given arm.
The question specifies that its zero belongs to the scale reading 42 at the marked tick.
2
Read the tick on that scale.
$θ = 42^{\circ}$
The 138 reading belongs to the opposite scale and does not measure from this starting arm.
3
Check its angle type.
$0^{\circ} < 42^{\circ} < 90^{\circ}$
The reading is less than a right angle, so the angle is acute.

Answer

$42^{\circ}$ , an acute angle.

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

Reflex.

The inequality $180^{\circ} < 215^{\circ} < 360^{\circ}$ places the angle beyond a straight angle but short of a full turn. It is reflex.

Keep practising

6 worksheet questions · 10 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

An angle measures a turn

Choose the zero before reading the scale

See the method in action.

Classify a turn

Locate the nearest angle boundaries.

Apply the classification.

Read the correct scale

Choose the scale starting at the given arm.

Read the tick on that scale.

Check its angle type.

Try it yourself.

Check your understanding

Keep practising