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Using the sum of the interior angles of a triangle

I can use the fact that the interior angles of any triangle sum to 180° to find the size of missing angles.

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Lesson 10 of 16

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Year 8

Using the sum of the interior angles of a triangle

I can use the fact that the interior angles of any triangle sum to 180° to find the size of missing angles.

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Lesson details

Key learning points

Missing angles in triangles can be found using the angle sum.
Missing angles in triangles can be found using the angle sum and other triangle properties.

Keywords

Interior angle - an angle formed inside a polygon by two of its edges.
Sum - the total when numbers are added together.

Common misconception

Assuming triangles are certain types because of how they look.

Unless there is notation or it has stated the type of triangle you cannot assume.

Pupils could create their own problems for peers. They may wish to look at combining triangles to make the problems more challenging.

Teacher tip

Licence

This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
The sum of 241, 68 and 192 is .

Correct Answer: 501, five hundred and one

Q2.
Simplify the following expression $$3x+5y-2x+9y+3x+12$$.

$$8x+14y+12$$

$$8x-14y+12$$

Correct answer: $$4x+14y+12$$

$$4x-14y+12$$

$$18xy+12$$

Q3.
A triangle DEF, where DE = 23 cm, DF = 23 cm and angle EDF is 45° is __________ triangle.

a scalene

Correct answer: an isosceles

an equilateral

a right-angled scalene

a right-angled isosceles

Q4.
Solve $$29=54-2x$$

Correct answer: $$x=12.5$$

$$x=-12.5$$

$$x=41.5$$

$$x=83$$

$$x=25$$

Q5.
Which of these are correct for the size of the angle marked $$n$$?

$$n=28$$

Correct answer: $$n=180-(28+131)$$

$$n=131$$

Correct answer: $$n=180-28-131$$

Q6.
Select the statements that best complete the following sentence. By tearing the corners off of a triangle and arranging them together at a point it you have...

Correct answer: ...shown that the three angles in a triangle sum to 180°.

Correct answer: ...demonstrated that the three angles in a triangle sum to 180°.

...proved that the three angles in a triangle sum to 180°.

Assessment exit quiz

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6 Questions

Q1.
The size of the angle $$x$$° is °.

Correct Answer: 38, thirty eight, 38°

Q2.
Match the two angles of a triangle with its third angle.

Correct Answer:60°, 60°,60°

Correct Answer:57°, 103°,20°

Correct Answer:90°, 27°,63°

Correct Answer:108°, 51°,21°

Correct Answer:51°, 98°,31°

Correct Answer:104°, 38°,38°

Q3.
In which of these triangles is there enough information for you to calculate the size of the missing angle?

Correct Answer: An image in a quiz

Q4.
The size of the angle $$x°$$ is °.

Correct Answer: 78, seventy eight

Q5.
Which of the following are calculations to find the value of $$y$$?

$$y=\frac{180+28}{2}$$

Correct answer: $$y=\frac{180-28}{2}$$

$$2y=\frac{180-28}{2}$$

Correct answer: $$y=\frac{1}{2}(180-28)$$

Q6.
Work out the value of $$m$$.

Correct answer: 12

180

Lesson appears in

UnitMaths / Geometrical properties: polygons

Maths

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Using the sum of the interior angles of a triangle

Using the sum of the interior angles of a triangle

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.The sum of 241, 68 and 192 is .

Q2.Simplify the following expression $$3x+5y-2x+9y+3x+12$$.

Q3.A triangle DEF, where DE = 23 cm, DF = 23 cm and angle EDF is 45° is __________ triangle.

Q4.Solve $$29=54-2x$$

Q5.Which of these are correct for the size of the angle marked $$n$$?

Q6.Select the statements that best complete the following sentence. By tearing the corners off of a triangle and arranging them together at a point it you have...

Assessment exit quiz

6 Questions

Q1.The size of the angle $$x$$° is °.

Q2.Match the two angles of a triangle with its third angle.

Q3.In which of these triangles is there enough information for you to calculate the size of the missing angle?

Q4.The size of the angle $$x°$$ is °.

Q5.Which of the following are calculations to find the value of $$y$$?

Q6.Work out the value of $$m$$.

Lesson appears in

UnitMaths / Geometrical properties: polygons

Maths

Q1.
The sum of 241, 68 and 192 is .

Q2.
Simplify the following expression $$3x+5y-2x+9y+3x+12$$.

Q3.
A triangle DEF, where DE = 23 cm, DF = 23 cm and angle EDF is 45° is __________ triangle.

Q4.
Solve $$29=54-2x$$

Q5.
Which of these are correct for the size of the angle marked $$n$$?

Q6.
Select the statements that best complete the following sentence. By tearing the corners off of a triangle and arranging them together at a point it you have...

Q1.
The size of the angle $$x$$° is °.

Q2.
Match the two angles of a triangle with its third angle.

Q3.
In which of these triangles is there enough information for you to calculate the size of the missing angle?

Q4.
The size of the angle $$x°$$ is °.

Q5.
Which of the following are calculations to find the value of $$y$$?

Q6.
Work out the value of $$m$$.