In the diagram, `ABCDE` is a regular pentagon. The diagonals `AC` and `BD` intersect at `F`.
- Show that the size of `/_ABC` is 108°. (1 mark)
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- Find the size of `/_BAC`. Give reasons for your answer. (2 marks)
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Show Worked Solution
| i. |  |
`text(Sum of all internal angles)`
`= (n-2) xx 180°`
`= (5-2) xx 180°`
`= 540°`
`:. /_ABC= 540/5= 108°`
ii. `BA = BC\ \ text{(equal sides of a regular pentagon)}`
`:. Delta BAC\ text(is isosceles)`
`/_BAC= 1/2 (180-108)=36^{\circ} \ \ \ text{(base angle of}\ Delta BAC text{)}`