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Math lesson plan · 8th grade (Year 9 in England) · 30 minutes

Use the exterior angle of a triangle

Geometry

CCSS 8.G.A.5England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures

Objective and success criteria

Students will: Use the exterior angle of a triangle.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Missing angles in triangles, including isosceles and algebra

Leads to: the next skill in this area.

Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 4 min

  • Quick retrieval from earlier learning (Missing angles in triangles, including isosceles and algebra). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. The angles of a triangle are x, 3x and 5x. What is the largest angle, in degrees? → 100Prompt: They add to 180°: 9x = 180.
  2. In a triangle, two angles are 37° and 70°. One side is extended to make an exterior angle next to the third angle. How big is that exterior angle? → 107Prompt: Find the third angle first, then use the straight line.
  3. In a triangle, two angles are 47° and 38°. One side is extended to make an exterior angle next to the third angle. How big is that exterior angle? → 85Prompt: Find the third angle first, then use the straight line.

Hook · 3 min

  • Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
  • Share the objective: Use the exterior angle of a triangle. Read the success criteria together.

I do: model it · 7 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: An exterior angle of a triangle is 106°. One of the two opposite interior angles is 44°. Find the other opposite interior angle.
  • Step 1: 106° − 44° = 62°
  • Answer: 62
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 6 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. An exterior angle of a triangle is 110°. One of the two opposite interior angles is 79°. Find the other opposite interior angle. → 31Prompt: The exterior angle equals the sum of the two opposite interior angles.
  2. In a triangle the two opposite interior angles are (x + 1)° and (2x + 20)°. The exterior angle is 84°. Find x. → 21Prompt: Exterior angle = sum of the two opposite interior angles.

You do: independent practice · 7 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 6 questions are on the student sheet below, with answers in the key.

Exit ticket · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. An exterior angle of a triangle is 90°. One of the two opposite interior angles is 50°. Find the other opposite interior angle. → 40Prompt: The exterior angle equals the sum of the two opposite interior angles.
  2. In a triangle the two opposite interior angles are (x + 9)° and (2x + 0)°. The exterior angle is 60°. Find x. → 17Prompt: Exterior angle = sum of the two opposite interior angles.

Watch out for

  • Thinking a square turned on its corner is no longer a square.
  • Reading the wrong scale on a protractor.

Support and stretch

Support

  • Review first: Missing angles in triangles, including isosceles and algebra.
  • Use concrete materials: rulers and protractors.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.

Free lesson plan from eurekami.com/lesson-plan-builder

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Use the exterior angle of a triangle

Name

Date

Score/ 6

  1. Question 1

    An exterior angle of a triangle is 82°. One of the two opposite interior angles is 26°. Find the other opposite interior angle.

    Answer

  2. Question 2

    In a triangle the two opposite interior angles are (x + 16)° and (2x + 14)°. The exterior angle is 108°. Find x.

    Answer

  3. Question 3

    An exterior angle of a triangle is 109°. One of the two opposite interior angles is 62°. Find the other opposite interior angle.

    Answer

  4. Question 4

    In a triangle the two opposite interior angles are (x + 18)° and (2x + 8)°. The exterior angle is 65°. Find x.

    Answer

  5. Question 5

    An exterior angle of a triangle is 92°. One of the two opposite interior angles is 25°. Find the other opposite interior angle.

    Answer

  6. Question 6

    In a triangle the two opposite interior angles are (x + 10)° and (2x + 0)°. The exterior angle is 67°. Find x.

    Answer

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Answer key: Use the exterior angle of a triangle

  1. 1. 56

  2. 2. 26

  3. 3. 47

  4. 4. 13

  5. 5. 67

  6. 6. 19