Primary 6 Foundation maths · Geometry · About 12 minutes
Find angles in composite figures without adding lines
Identify the relevant property before combining angle facts. Do not invent extra lines or equalities.
Start the interactive lesson →Open practice activity
What you will learn
- Find angles in composite figures without adding lines
Models used: number sentences, stories, tables.
Before you start
Make the known corners work for you
Two corners of this triangle are 50° and 60°. What turn is left for the third corner?
The labels belong to the inside corners. The question mark is the corner we still need to find.
Two corners of this triangle are 50° and 60°. What turn is left for the third corner?
Equal sides, parallel sides and complete angle sums supply different information. Use only what is given or follows from the named shape.
The labels belong to the inside corners. The question mark is the corner we still need to find.
The three inside angles of a triangle add to 180°. The two known corners use 110°.
50° + 60° = 110°
The labels belong to the inside corners. The question mark is the corner we still need to find.
The remaining corner is 70°. Check by adding all three.
180° − 110° = 70°
What did the picture help us see?
The remaining corner is 70°. Check by adding all three.
Worked example: A new example, together
An isosceles triangle has vertex angle 60°. Find each equal base angle.
| Known angle | Relationship |
|---|---|
| 60° | angles in the named geometric figure |
Use only the stated lines and properties. Read each value with the heading above its column.
Identify the relevant property before combining angle facts. Do not invent extra lines or equalities.
Equal sides face equal angles, and all three angles total 180°.
Use only the stated lines and properties Known angle Relationship 60° angles in the named geometric figure Use only the stated lines and properties. Read each value with the heading above its column.
The three interior angles of a triangle total 180°.
Use only the stated lines and properties Known angle Relationship 60° angles in the named geometric figure An isosceles triangle has vertex angle 60°. Find each equal base angle.
60 degrees
Use only the stated lines and properties. Read each value with the heading above its column.
The three interior angles of a triangle total 180°.
Use only the stated lines and properties Known angle Relationship 60° angles in the named geometric figure Use only the stated lines and properties. Read each value with the heading above its column.
The two equal base angles share 180 − 60 = 120° equally.
Use only the stated lines and properties Known angle Relationship 60° angles in the named geometric figure Use only the stated lines and properties. Read each value with the heading above its column.
The requested angle is 60°.
Use only the stated lines and properties Known angle Relationship 60° angles in the named geometric figure Use only the stated lines and properties. Read each value with the heading above its column.
Check the result against the question we started with.
60 + 2 × 60 = 180°.
We found 60 degrees. Equal sides face equal angles, and all three angles total 180°.
Use only the stated lines and properties Known angle Relationship 60° angles in the named geometric figure
Common mistakes to discuss
- Measuring the diagram. Diagrams are not to scale. Use the marked lengths, equal sides and known angle facts.
Check your understanding
- Find angles in composite figures without adding lines
- connect shape properties with justified angle calculations
- 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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