Interior angle of a regular pentagon is 108 degrees, and each angle of a square is 90 degrees. At vertex A, angle QAB =360−108−90=162 degrees. Since AQ = AE = AB (square side equals pentagon side), triangle AQB is isoceles. Base angles: (180−162)/2=9 degrees. So angle AQB =9 degrees.
CUET UG 2023 — General Test Geometry
2023mcqhard
In the figure, ABCDE and AEPQ are a regular pentagon and a square respectively. What is the measure of angle AQB ?
Official previous-year question
Held on 5 Jun 2023 · Verified 13 Jul 2026.
Options
- A
9 degrees
- B
14 degrees
- C
18 degrees
- D
19 degrees
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