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      Using the sum of the interior angles of a triangle

      Lesson details

      Learning outcome

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

      Key learning points

      1. Missing angles in triangles can be found using the angle sum.
      2. 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.

      Teacher tip

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

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      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 $$n$$?

      An image in a quiz
      $$n=28$$
      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...

      An image in a quiz
      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°.

      6 Questions

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

      An image in a quiz
      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?

      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz

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

      An image in a quiz
      Correct Answer: 78, seventy eight

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

      An image in a quiz
      $$y=\frac{180+28}{2}$$
      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 $$m$$.

      An image in a quiz
      10
      Correct answer: 12
      60
      180

      To help you plan your 8 maths lesson on: Using the sum of the interior angles of a triangle, download all teaching resources for free and adapt to suit your pupils' needs...