Primary 5 maths · Geometry · About 12 minutes
Find unknown angles
Locate the common vertex, the given lines and the complete turn being filled.
Start the interactive lesson →Open practice activity
What you will learn
- Find unknown angles
Models used: number sentences, stories, tables.
Before you start
Use the turn you already know
A straight line makes a half-turn. That whole turn is 180 degrees.
The straight line is the whole half-turn. The coloured arcs show its two parts.
A straight line makes a half-turn. That whole turn is 180 degrees.
A straight turn, a full turn and vertically opposite angles use different facts. The markings decide which fact applies.
The straight line is the whole half-turn. The coloured arcs show its two parts.
The blue part uses 60 degrees. The orange part must fill the space left over.
The unknown angle must fill exactly the part of the straight turn that the known angle does not use.
The straight line is the whole half-turn. The coloured arcs show its two parts.
Subtract the known part from the whole turn.
180° − 60° = 120°
The unknown angle must fill exactly the part of the straight turn that the known angle does not use.
What did the picture help us see?
Subtract the known part from the whole turn.
Worked example: A new example, together
Two straight lines cross. One angle is 90°. Find the vertically opposite angle.
| Known angle | Relationship |
|---|---|
| 90° | opposite at an intersection |
Use the marked relationship. Read each value with the heading above its column.
Locate the common vertex, the given lines and the complete turn being filled.
Two intersecting straight lines create equal vertically opposite angles.
Use the marked relationship Known angle Relationship 90° opposite at an intersection Use the marked relationship. Read each value with the heading above its column.
Vertically opposite angles are equal.
Use the marked relationship Known angle Relationship 90° opposite at an intersection Two straight lines cross. One angle is 90°. Find the vertically opposite angle.
90 degrees
Use the marked relationship. Read each value with the heading above its column.
Vertically opposite angles are equal.
Use the marked relationship Known angle Relationship 90° opposite at an intersection Use the marked relationship. Read each value with the heading above its column.
The angle across the vertex matches 90°.
Use the marked relationship Known angle Relationship 90° opposite at an intersection Use the marked relationship. Read each value with the heading above its column.
x = 90°.
Use the marked relationship Known angle Relationship 90° opposite at an intersection Use the marked relationship. Read each value with the heading above its column.
Check the result against the question we started with.
The opposite angle equals 90°.
We found 90 degrees. Two intersecting straight lines create equal vertically opposite angles.
Use the marked relationship Known angle Relationship 90° opposite at an intersection
Common mistakes to discuss
- Measuring the drawing. Diagrams are not drawn to scale. Use the stated angles and the angle facts rather than a protractor on the picture.
Check your understanding
- Find unknown angles
- justify an unknown angle with the stated angle relationship
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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