Foundation June 2019 Paper 2 Q8
8
(a) The interior angle of a regular pentagon is \(108^\circ\)
Work out the sum of the five reflex angles at the vertices of a regular pentagon. [3 marks]
Not drawn accurately
Omar asks Harry,
“How many lines of symmetry does a pentagon have?”
Harry assumes it is a regular pentagon.
His answer is 5.
(b) Draw the lines of symmetry on this regular pentagon. [1 mark]
(c) Omar then says,
“What if the pentagon is not regular?”
For a pentagon that is not regular, what is true about the number of lines of symmetry?
Tick one box. [1 mark]
- There must be 0
- There could be 0 or 1
- There could be 0, 1 or 2
- There could be any number up to 5
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(360 - 108\) or 252 | M1 | oe eg \(360 \div 5 + 180\) may be on diagram |
| their \(252 \times 5\) | M1dep | oe eg \(5 \times (180 - 108) + 5 \times 180\) or \(5 \times 72 + 5 \times 180\) or \(5 \times (72 + 180)\) |
| 1260 | A1 | SC1 answer 540 |
| Alternative method 2 | ||
| \(5 \times 360\) or 1800 and \(5 \times 108\) or 540 | M1 | |
| \(5 \times 360 - 5 \times 108\) or \(1800 - 540\) | M1dep | oe |
| 1260 | A1 | SC1 answer 540 |
Additional guidance
| Allow 252 seen on the diagram or in the working even if not used | M1 |
| Answer | Mark | Comments |
|---|---|---|
Line through each vertex to the midpoint of the opposite side | B1 | mark intention |
Additional guidance
Allow dotted lines
| Answer | Mark | Comments |
|---|---|---|
| There could be 0 or 1 | B1 |