In ΔPQR, if 4∠P = 5∠Q = 20∠R, then the value of ∠Q is:

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Given: 4∠P = 5∠Q = 20∠R = k (some constant)

Let 4∠P = 5∠Q = 20∠R = k.

Then,  
∠P = k/4,   
∠Q = k/5,  
∠R = k/20.

Sum of angles in a triangle is 180°:  
∠P + ∠Q + ∠R = 180°  
=> k/4 + k/5 + k/20 = 180

Find common denominator: 20  
=> (5k + 4k + k)/20 = 180   
=> (10k)/20 = 180  
=> k/2 = 180  
=> k = 360

Now, ∠Q = k/5 = 360/5 = 72°.

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