Special Properties, SMB-031 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) --- 3 WORK AREA LINES (style=lined) --- Find the size of `/_BAC`. Give reasons for your answer. (2 marks) --- 5 WORK AREA LINES (style=lined) --- Show Answers Only `text(See Worked Solutions)` `36°` 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{)}`