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F1 Koda Shraddha 10.03.2020 D6

Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above.
The value of θ, in degrees, is ______

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  1. 36
  2. 45
  3. 72
  4. 108

Answer (Detailed Solution Below)

Option 1 : 36
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Detailed Solution

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Given:

PR = PS = QS = QT = RT 

F1 Killi 8.3.21 Pallavi D22

Then ABCDEF will be regular pentagon

∠EAB = Sum of angles of pentagon/5

⇒ ∠EAB = 540°/5 = 108° 

⇒ ∠PAB = 180° – 108° = 72°

⇒ θ  + ∠PAB + ∠PBA = 180

⇒ θ  + 72 + 72 = 180°

⇒ θ  = 36°

Option (a) is correct.

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