Angle relationships – Grade 8 math lesson
Lesson 12 of 16 in the Grade 8 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 8 (ages 13–14) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 8 (ages 13–14)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why do co-interior angles add up to 180°?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Measuring with a protractor when the diagram is not to scale. Use angle facts and write the reason.
- Mixing up alternate and co-interior angles. Z shape: equal. C shape: add to 180°.
Tip for home: Find parallel lines and crossing lines in windows, railings and roads.
What your child will learn
Learning goal: use angle facts and angles in parallel lines to find missing angles, giving reasons.
Success looks like
- I can use basic angle facts.
- I can use angles in parallel lines.
- I can give reasons for each step.
Key words
- vertically opposite
- equal angles opposite each other where two lines cross
- alternate angles
- equal angles in a Z shape
- corresponding angles
- equal angles in an F shape
- co-interior angles
- angles in a C shape that add to 180°
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Draw two parallel lines and a crossing line, measure all eight angles and spot which are equal.
The big ideas (for the adult)
Angles on a straight line add up to 180°; angles around a point add up to 360°; vertically opposite angles are equal.
Angles in a triangle add up to 180°. The two base angles of an isosceles triangle are equal.
Where a line crosses parallel lines: alternate angles are equal, corresponding angles are equal, and co-interior angles add up to 180°.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 8 math lessons
- Repeating decimals
- Scientific notation
- Laws of exponents
- Square roots and cube roots
- Simplifying expressions
- Solving equations
- Systems of equations
- Arithmetic and geometric sequences
- Linear functions and slope
- Functions
- Graphing functions
- Volume and surface area
- The Pythagorean theorem
- Transformations
- Scatter plots and lines of fit
Curriculum
Common Core State Standards 8.G.A.5: “Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.”
Common Core State Standards HSG.CO.C.9: “Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.