Geometry

Miscellaneous

Hard

In the figure, ABCDE and AEPQ are a regular pentagon and a square respectively. What is the measure of angle AQB ?

9 degrees

14 degrees

18 degrees

19 degrees

✅ Correct Option: 1

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.

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Match List - I with List - II.

List - I (Shape)	List - II (Area)
(A) Square	(I) $\pi a^2$
(B) Triangle	(II) $b \times h$
(C) Circle	(III) $a \times a$
(D) Parallelogram	(IV) $\frac{1}{2} b \times h$

Choose the correct answer from the options given below :

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In the figure, ABCDE and AEPQ are a regular pentagon and a square respectively. What is the measure of angle AQB ?

Solution

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