In the figure, ABCDE and AEPQ are a regular pentagon and a square respectively. What is the measure of ∠AQB?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 9°
The square and the pentagon share the side AE, so AQ = AE = AB and triangle QAB is isosceles. Its base angles are found once the angle at A is known; the angles round the point A add up to 360°.
Each interior angle of a regular pentagon \(\displaystyle =\frac{(5-2)\times180^\circ}{5}=108^\circ\), so ∠EAB = 108°
∠QAE = 90° (angle of the square)
∠QAB \(=360^\circ-90^\circ-108^\circ=162^\circ\)
∠AQB = ∠ABQ \(\displaystyle =\frac{180^\circ-162^\circ}{2}=9^\circ\)
