New
New
Year 10
Higher

Forming equations with angles

I can form and solve equations using my knowledge of angles and polygons.

New
New
Year 10
Higher

Forming equations with angles

I can form and solve equations using my knowledge of angles and polygons.

Lesson details

Key learning points

  1. Missing angles can be found in polygons using knowledge of exterior and interior angles.
  2. A missing angle can be represented with an unknown.
  3. Algebraic statements can be written about the missing angles in polygons.

Common misconception

Alternate angles are always equal to each other.

Alternate angles are equal when a transversal intersects parallel lines. If the transversal intersects a pair of lines that are not parallel then the alternate angles will not be equal.

Keywords

  • 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.

When forming the equations, pupils can be asked to state which angle or shape facts they are using in order to generate the equation. This will help to reinforce the facts and support pupil understanding regarding why the equation can be formed.
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 exterior angles of any polygon __________ sum to 360°.
Correct answer: always
sometimes
never
Q2.
The interior angles of any polygon __________ sum to 360°.
always
Correct answer: sometimes
never
Q3.
An interior angle and its adjacent exterior angle __________ sum to 360°.
always
sometimes
Correct answer: never
Q4.
A regular polygon has exterior angles of size 24°. The polygon has sides.
Correct Answer: 15, fifteen
Q5.
The size of each exterior angle of a regular octagon is °.
Correct Answer: 45
Q6.
The regular polygon that has interior angles that are equal to its exterior angles is a .
Correct Answer: square, regular quadrilateral, regular 4-sided polygon

6 Questions

Q1.
Match each description to the correct statement.
An image in a quiz
Correct Answer:unsimplified expression for angle sum,5$$x$$ + 46 + 74

5$$x$$ + 46 + 74

Correct Answer:simplified expression for angle sum,5$$x$$ + 120

5$$x$$ + 120

Correct Answer:equation for angle sum,5$$x$$ + 120 = 180

5$$x$$ + 120 = 180

Correct Answer:solution for $$\text{ }x$$,$$x$$ = 12

$$x$$ = 12

Correct Answer:angles in triangle,46°, 60°, 74°

46°, 60°, 74°

Q2.
Find the value of $$x$$.
An image in a quiz
10
11.5
Correct answer: 13
15
Q3.
Find the value of $$x$$.
An image in a quiz
Correct answer: 14
23
28
32
Q4.
Find the value of $$x$$. Give your answer correct to 3 significant figures.
An image in a quiz
10.3
15.4
Correct answer: 16.8
18.2
Q5.
The value of $$x$$ is .
An image in a quiz
Correct Answer: 147
Q6.
Find an equation for $$y$$ in terms of $$x$$.
An image in a quiz
$$y=62-x$$
$$y=79+2x$$
Correct answer: $$y=79-2x$$
$$(2y+3)+(4x+2)+107=360$$
$$(2y+3)+(4x+2)+197$$