Theory question 105
Angles and PolygonsABCDE 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.
Show the model answer
Model answer
(i) Sum of interior angles = (5 − 2) × 180° = 540°; each angle = 540° ÷ 5 = 108°
(ii) ∠XAE = 90° (rectangle), so ∠BAX = 108° − 90° = 18°
In triangle ABX: ∠BXA = 180° − 108° − 18° = 54°
Explanation
Draw the figure: the rectangle shares side AE with the pentagon.