Use the angle sum of a triangle

What you will learn

• Use the angle sum of a triangle

Models used: number sentences, stories, diagrams.

Before you start

• Use rectangle, square and triangle properties

Make the known corners work for you

Two corners of this triangle are 50° and 60°. What turn is left for the third corner?

1. 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.

2. 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°

3. 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°

Worked example: A new example, together

A triangle has angles 30° and 60°. Find its third angle.

1. The labels belong to the inside corners. The question mark is the corner we still need to find.

   Identify the relevant property before combining angle facts. Do not invent extra lines or equalities.

   The three interior angles of any triangle sum to 180°.

2. The labels belong to the inside corners. The question mark is the corner we still need to find.

   The three interior angles of a triangle total 180°.

   A triangle has angles 30° and 60°. Find its third angle.

   90 degrees

3. The labels belong to the inside corners. The question mark is the corner we still need to find.

   The three interior angles of a triangle total 180°.

4. The labels belong to the inside corners. The question mark is the corner we still need to find.

   The known angles total 90°.

5. The labels belong to the inside corners. The question mark is the corner we still need to find.

   The requested angle is 90°.

6. The labels belong to the inside corners. The question mark is the corner we still need to find.

   Check the result against the question we started with.

   30 + 60 + 90 = 180°.

   We found 90 degrees. The three interior angles of any triangle sum to 180°.

Common mistakes to discuss

• The angle sum grows with the triangle. The three angles of any triangle total 180°, whatever its size. With 50° and 60°, the third is 70°.

Check your understanding

• Use the angle sum of a triangle
• 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.