In the given figure lines AP and OQ intersect at G If ang AGO ang PGF 70 deg and ang PGQ 40 deg Find...........

Quantitative Aptitude ( CCS) Geometry

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In the given figure lines AP and OQ intersect at G. If ∠AGO + ∠PGF = 70° and ∠PGQ = 40°. Find the angle value of ∠PGF.

31°

35°

30°

20°

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Explanation:

As AP is a straight line and rays GO and GF stands on it.
∴ ∠AGO + ∠OGF + ∠PGF = 180°
⇒ (∠AGO + ∠PGF) + ∠OGF = 180°
⇒ 70° + ∠OGF = 180°
⇒ ∠OGF = 180° – 70°
⇒ ∠OGF = 110°
As, OQ is a straight line, rays GF and GP stands on it.
∠OGF + ∠PGF + ∠PGQ = 180°
Putting the value of ∠OGF & ∠PGQ
110° + ∠PGF + 40° = 180°
∠PGF = 180° – 150° = 30°