Question
Download Solution PDFIn the figure, OP⊥OA and OQ⊥OB. Find ∠POQ if ∠AOB = 20o
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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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