Straight-line angles | Year 6

01 / LEARN

Understand the idea.

A straight angle is a half-turn

A straight angle is a half-turn, measuring $180^{\circ}$ . Angles are adjacent when they share a vertex and one arm without overlapping. When adjacent parts fill a straight angle, their sizes must add to $180^{\circ}$ .

Treat the straight angle as a whole and the labelled angles as its parts. To find a missing part, subtract the known part from $180^{\circ}$ . The lengths of the drawn arms do not determine the angle’s size.

More than two parts

A straight angle can have more than two parts. Add all the known angles that lie inside the same half-turn, then subtract their total from $180^{\circ}$ . Do not include an angle on the other side of the line.

Finish by adding your result to the known parts. The total must be $180^{\circ}$ . Give the degree symbol and state the straight-line rule so your answer is supported by geometry rather than the appearance of the drawing.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Two adjacent angles

A 65° angle and x fill the straight angle shown. Find x.

Worked solution

1
Write the straight-angle total.
$65^{\circ} + x = 180^{\circ}$
The two adjacent angles fill one straight angle.
2
Subtract the known part.
$x = 180^{\circ} - 65^{\circ} = 115^{\circ}$
Removing the known 65-degree angle leaves the missing part.
3
Check the two parts.
$65^{\circ} + 115^{\circ} = 180^{\circ}$
The result completes the required half-turn.

Answer

115°

EXAMPLE 02

Three adjacent parts

A straight angle is split into 90°, 35° and x. Find x.

Worked solution

1
Add the two known parts.
$90^{\circ} + 35^{\circ} = 125^{\circ}$
Both labelled angles lie within the same straight angle.
2
Find the remaining part.
$x = 180^{\circ} - 125^{\circ} = 55^{\circ}$
All three adjacent parts together must total 180 degrees.
3
Check the whole angle.
$90^{\circ} + 35^{\circ} + 55^{\circ} = 180^{\circ}$
Each part is counted once and the straight-angle total is restored.

Answer

55°

03 / YOUR TURN

Try it yourself.

Check your understanding

Two adjacent angles form a straight angle. One is 48°. Find the other.

Show answer & reasoning

132°

The adjacent angles fill a straight angle, so the missing part is $180^{\circ} - 48^{\circ} = 132^{\circ}$ . Checking gives $48^{\circ} + 132^{\circ} = 180^{\circ}$ .

Keep practising

6 worksheet questions · 9 marks

Open worksheet Worked solutions

Read the questions online

Two adjacent angles form a straight angle. One is $72^{\circ}$ . Find the other.
1 mark
One of two adjacent angles on a straight line is $137^{\circ}$ . Find its neighbour.
1 mark
A straight angle is split into $40^{\circ}$ , $65^{\circ}$ and $x$ . Find $x$ .
2 marks
Two equal angles fill a straight angle. Find each angle.
1 mark
Can two adjacent angles of $95^{\circ}$ and $85^{\circ}$ fill a straight angle? Explain.
2 marks
Noah says the angle next to a $48^{\circ}$ angle on a straight line is $228^{\circ}$ , because $180 + 48 = 228$ . Correct his method and answer.
2 marks

Read the worked solutions

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

Two adjacent angles form a straight angle. One is $72^{\circ}$ . Find the other.
1 mark
$180^{\circ} - 72^{\circ} = 108^{\circ}$ .
$108^{\circ}$
One of two adjacent angles on a straight line is $137^{\circ}$ . Find its neighbour.
1 mark
$180^{\circ} - 137^{\circ} = 43^{\circ}$ .
$43^{\circ}$
A straight angle is split into $40^{\circ}$ , $65^{\circ}$ and $x$ . Find $x$ .
2 marks
$40^{\circ} + 65^{\circ} = 105^{\circ}$ .
$180^{\circ} - 105^{\circ} = 75^{\circ}$ .
$75^{\circ}$
Two equal angles fill a straight angle. Find each angle.
1 mark
$180^{\circ}$ shared equally between two angles gives $90^{\circ}$ each.
$90^{\circ}$
Can two adjacent angles of $95^{\circ}$ and $85^{\circ}$ fill a straight angle? Explain.
2 marks
$95^{\circ} + 85^{\circ} = 180^{\circ}$ , so they can fill the half-turn.
Yes.
Noah says the angle next to a $48^{\circ}$ angle on a straight line is $228^{\circ}$ , because $180 + 48 = 228$ . Correct his method and answer.
2 marks
The parts together total $180^{\circ}$ .
$180^{\circ} - 48^{\circ} = 132^{\circ}$ .
$48^{\circ} + 132^{\circ} = 180^{\circ}$ .
Subtract instead: the missing angle is $132^{\circ}$ .

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Year 6 angle relationships: straight-line angles, angles around a point, vertically opposite angles and connected reasoning.

Official curriculum source ↗

In this lesson

Understand the idea.

A straight angle is a half-turn

More than two parts

See the method in action.

Two adjacent angles

Write the straight-angle total.

Subtract the known part.

Check the two parts.

Three adjacent parts

Add the two known parts.

Find the remaining part.

Check the whole angle.

Try it yourself.

Check your understanding

Keep practising