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.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(i) Sum of interior angles of a regular polygon = \((2n - 4) \times 90^\circ\)
For a pentagon, \((2(5) - 4) \times 90^\circ = 6 \times 90^\circ = 540^\circ\)
Interior angle = \(\frac{540^\circ}{5} = 108^\circ\)
(ii) < BXA = 108^\circ - 90^\circ = 18^\circ
< ABX = 108^\circ (as shown above)
\(\therefore < BXA = 180^\circ - (108^\circ + 18^\circ) = 54^\circ\)
Source: Myschool Past Questions Archive (Record #54610)