New
New
Year 10
Higher

Problem solving with angles

I can use my knowledge of angles to solve problems.

New
New
Year 10
Higher

Problem solving with angles

I can use my knowledge of angles to solve problems.

Lesson details

Key learning points

  1. Problems can be solved using parallel line angle facts.
  2. Problems can be solved using interior and exterior angles of polygons.
  3. Problems can be solved and the solution justified using angle facts.

Common misconception

Lines cannot be added to the given diagram.

Often adding additional or found information to a given diagram can help progress towards a solution. Pupils should not be afraid to extend given line segments nor add notation if appropriate.

Keywords

  • Alternate angles - Alternate angles are a pair of angles both between or both outside two line segments that are on opposite sides of the transversal that cuts them.

  • Interior angle - An interior angle is an angle formed inside a polygon by two of its edges.

  • Exterior angle - An exterior angle is an angle on the outside of a polygon between an extension of an edge and the adjacent edge.

There are often multiple ways to find the size of unknown angles. Pupils can be encouraged to find as many ways as they can to justify their answers using the different angle facts. They could also identify which angle facts would not be useful for each problem.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
The sum of exterior angles for any polygon sum to...
90°
180°
270°
Correct answer: 360°
720°
Q2.
Which of these describe angles that are definitely equal to each other?
Correct answer: Base angles of an isosceles triangle
Co-interior angles between parallel sides
Exterior angles of a polygon
Correct answer: Interior angles of a regular polygon
Correct answer: Opposite angles in a parallelogram
Q3.
The value of $$x$$ is .
An image in a quiz
Correct Answer: 6, six
Q4.
What do the interior angles of a 72 sided polygon sum to?
102.22...°
360°
Correct answer: 12 600°
12 960°
36 000°
Q5.
Find the value of $$x$$. (Note: The diagram is not drawn to scale)
An image in a quiz
-2
-0.5
0.5
Correct answer: 1
2
Q6.
Find the value of $$y$$
An image in a quiz
$$75 + 4x$$
Correct answer: 150
300
422
$$422-4x$$

6 Questions

Q1.
The value of $$x$$ is .
An image in a quiz
Correct Answer: 115, one hundred and fifteen
Q2.
Find the value of $$x$$.
An image in a quiz
Correct answer: 35
70
110
Q3.
The value of $$x$$ is .
An image in a quiz
Correct Answer: 40, forty
Q4.
The value of $$x$$ is .
An image in a quiz
Correct Answer: 39, thirty nine
Q5.
The diagram is not drawn accurately. AC is a line segment and ∠DBA : ∠CBD = 3 : 1. Which equation can be formed from this information?
An image in a quiz
$$2x = 180$$
$$3x = 180$$
Correct answer: $$4x = 180$$
$$5x = 180$$
Q6.
The value of $$x$$ is .
An image in a quiz
Correct Answer: 126, one hundred and twenty six