Angles on lines and around points | Year 7

01 / LEARN

The idea, step by step

Choose the total that the diagram gives

Adjacent angles share a vertex and one arm, and their interiors do not overlap. If their outer arms form a straight line, together they make a half-turn. Their total is $180^{\circ}$ . Do not use this rule merely because two angles happen to touch.

First identify the straight outer line. Write a total such as $a + b = 180^{\circ}$ , then subtract the known angle. If a right-angle marker is shown instead, the total is $90^{\circ}$ .

a + b = 180^{\circ}

A complete turn has no gap

All the non-overlapping angles around a point add to $360^{\circ}$ , provided they cover the whole turn exactly once. Add all the known angles before subtracting from 360.

An angle drawn as a large reflex region is still just one part of the turn. Read the marked region carefully, and finish with a reason: angles around a point, angles on a straight line or angles in a right angle.

A common trap

Any two angles sharing a vertex must add to 180 degrees.

Instead: They add to 180 degrees only when they are adjacent and their outer arms form a straight line. Otherwise use the actual marked relationship.

02 / WORKED EXAMPLES

See the thinking

Example 1

Missing angle on a line

The two marked angles lie on a straight line. Find $x$ .

Their total is $180^{\circ}$ .
$x + 127^{\circ} = 180^{\circ}$ .
$x = 180^{\circ} - 127^{\circ} = 53^{\circ}$ .

x = 53^{\circ}

Example 2

Three angles around one point

Three angles around a point are $96^{\circ}$ , $118^{\circ}$ and $y$ . Find $y$ .

A full turn is $360^{\circ}$ .
The known angles total $96 + 118 = 214$ degrees.
$y = 360^{\circ} - 214^{\circ} = 146^{\circ}$ .

y = 146^{\circ}

Check your understanding

A right angle is split into $32^{\circ}$ and $x$ . Find $x$ .

Show answer

$58^{\circ}$ .

The total is 90 degrees, not 180: $90 - 32 = 58$ .

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Two adjacent angles on a straight line are $148^{\circ}$ and $a$ . Find $a$ .
2 marks
Four angles around a point are $85^{\circ}$ , $110^{\circ}$ , $74^{\circ}$ and $b$ . Find $b$ .
2 marks
Three equal adjacent angles fill a straight angle. Find the size of each.
2 marks
An angle of $54^{\circ}$ and angle $c$ fill a right angle. Find $c$ .
2 marks
A robot turns $135^{\circ}$ clockwise, then continues clockwise until it has completed one full turn. How far is the second turn?
2 marks
Alex subtracts $72^{\circ}$ from $360^{\circ}$ to find the adjacent angle on a straight line. Explain the error and give the correct answer.
3 marks

Read the worked solutions

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

Two adjacent angles on a straight line are $148^{\circ}$ and $a$ . Find $a$ .
2 marks
$a = 180^{\circ} - 148^{\circ} = 32^{\circ}$ .
$32^{\circ}$ .
Four angles around a point are $85^{\circ}$ , $110^{\circ}$ , $74^{\circ}$ and $b$ . Find $b$ .
2 marks
$85 + 110 + 74 = 269$ .
$b = 360^{\circ} - 269^{\circ} = 91^{\circ}$ .
$91^{\circ}$ .
Three equal adjacent angles fill a straight angle. Find the size of each.
2 marks
Their total is $180^{\circ}$ .
$180 \div 3 = 60$ .
$60^{\circ}$ .
An angle of $54^{\circ}$ and angle $c$ fill a right angle. Find $c$ .
2 marks
$c = 90^{\circ} - 54^{\circ} = 36^{\circ}$ .
$36^{\circ}$ .
A robot turns $135^{\circ}$ clockwise, then continues clockwise until it has completed one full turn. How far is the second turn?
2 marks
The full turn is $360^{\circ}$ .
$360 - 135 = 225$ . The second turn is reflex.
$225^{\circ}$ .
Alex subtracts $72^{\circ}$ from $360^{\circ}$ to find the adjacent angle on a straight line. Explain the error and give the correct answer.
3 marks
The outer arms form a straight line, not a full turn.
$180^{\circ} - 72^{\circ} = 108^{\circ}$ .
The total should be 180 degrees; the missing angle is $108^{\circ}$ .

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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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