In the figure, OPOA and OQOB. Find POQ if ∠AOB = 20o

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MP Police Constable 2023 Official Paper (Held On: 01 Sept, 2023 Shift 1)
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  1. 20°
  2. 30°
  3. 40°
  4. 10°

Answer (Detailed Solution Below)

Option 1 : 20°
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Detailed Solution

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Given:

OP ⊥ OA ⇒ ∠POA = 90°

OQ ⊥ OB ⇒ ∠QOB = 90°

∠AOB = 20°

Formula Used:

Angle addition postulate

Calculations:

From the figure, the angle ∠POA is composed of ∠POB and ∠AOB.

⇒ ∠POA = ∠POB + ∠AOB

⇒ 90° = ∠POB + 20°

⇒ ∠POB = 90° - 20°

⇒ ∠POB = 70°

Similarly, the angle ∠QOB is composed of ∠POQ and ∠POB.

⇒ ∠QOB = ∠POQ + ∠POB

⇒ 90° = ∠POQ + 70°

⇒ ∠POQ = 90° - 70°

⇒ ∠POQ = 20°

∴ The measure of ∠POQ is 20°.

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