ABCDE is a regular pentagon and a rectangle AXYE is drawn on the side AE such that the vertices X and Y lie on the sides BC and CD respectively. Calculate the size of
(i) an interior angle of the pentagon ;
(ii) < BXA.
Explanation
(i) Sum of interior angles of a regular polygon = ((2n – 4) times 90°)
For a pentagon, ((2(5) – 4) times 90° = 6 times 90° = 540°)
Interior angle = (frac{540°}{5} = 108°)
(ii) < BXA = 108° – 90° = 18°
< ABX = 108° (as shown above)
(therefore < BXA = 180° – (108° + 18°) = 54°)