New
New
Year 10
Higher

Checking and securing understanding of interior angles

I can find the interior angle of any regular polygon or deduce the interior angle of an irregular polygon.

New
New
Year 10
Higher

Checking and securing understanding of interior angles

I can find the interior angle of any regular polygon or deduce the interior angle of an irregular polygon.

Lesson details

Key learning points

  1. Any polygon can be split into triangles.
  2. Using these triangles you can demonstrate the rule for the interior angle sum of a polygon.
  3. A missing interior angle in any polygon can be found.
  4. The number of sides in a regular polygon can be determined from the size of the interior angle.
  5. The sum of the interior angles is the same, regardless of whether the polygon is regular.

Common misconception

The size of an interior angle in a regular shape cannot be found unless the size of the other angles are given.

A regular shape has the property that all of its interior angles are equal in size. This means that the size of each interior angle is very easy to find if, for example, the sum of the interior angles is known.

Keywords

  • Polygon - A polygon is a flat (2D), closed figure made up of straight line segments.

  • Regular - A regular polygon has sides that are all equal and interior (inside) angles that are all equal.

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

The third learning cycle utilises circular geoboards. Pupils would benefit from having access to these if possible so that they can investigate independently. However, they can still access the learning without them.
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.
Angles that meet at a single point on a straight line sum to °.
Correct Answer: 180, one hundred and eighty
Q2.
Angles are __________ if they sum to 180°.
conjugate
equal
similar
Correct answer: supplementary
Q3.
Two angles meet to form a straight line. One angle is 60°. The other angle is °.
Correct Answer: 120, hundred and twenty
Q4.
Squares and equilateral triangles are examples of __________ polygons.
congruent
irregular
Correct answer: regular
similar
Q5.
A regular octagon has an edge with length 5 cm. Therefore, its perimeter is cm.
Correct Answer: 40, forty, 40cm
Q6.
A regular decagon has a perimeter of 40 cm. Therefore, each of its edges are of length cm.
Correct Answer: 4, four, 4 cm

6 Questions

Q1.
Two of the interior angles of a triangle are 80° and 45°. The size of the third interior angle is °.
Correct Answer: 55, fifty five
Q2.
The interior angles of a pentagon sum to °.
Correct Answer: 540, five hundred a forty
Q3.
Each interior angle of a regular hexagon is °.
Correct Answer: 120, one hundred and twenty
Q4.
A regular polygon has interior angles of size 150°. The polygon has sides.
Correct Answer: 12, twelve
Q5.
Which of these interior angles are possible in a regular polygon?
72°
Correct answer: 135°
Correct answer: 140°
Correct answer: 144°
180°
Q6.
One of the interior angles in an isosceles triangle is 70°. Which are possible sizes for one of the other interior angles?
25°
Correct answer: 40°
Correct answer: 55°
Correct answer: 70°
85°