In fig. ∠ACB = 40°, find ∠OAB

1.	In fig. ∠ACB = 40°, find ∠OAB
Answer» ∴ ∠ACB = 40° We know that angle subtended by arc of a circle at center is double the angle at remaining part. ∴ ∠AOB = 2∠ACB = 2 × 40° = 80° ⇒ ∠AOB = 80° ∵ OA = OB = radius of circle ∴ In ∆AOB ∠OAB + ∠OBA + ∠AOB = 180° ∵ Angles opposite to equal sides are equal. ∴ ∠OAB = ∠OBA ⇒ ∠OAB + ∠OAB + 80° = 180° ⇒ 2∠OAB = 180° – 80° ⇒ ∠OAB = \(\frac { { 100 }^{ \circ } }{ 2 } \) ⇒ ∠OAB = 50°

Answer»

∴ ∠ACB = 40°

We know that angle subtended by arc of a circle at center is double the angle at remaining part.

∴ ∠AOB = 2∠ACB

= 2 × 40°

= 80°

⇒ ∠AOB = 80°

∵ OA = OB = radius of circle

∴ In ∆AOB

∠OAB + ∠OBA + ∠AOB = 180°

∵ Angles opposite to equal sides are equal.

∴ ∠OAB = ∠OBA

⇒ ∠OAB + ∠OAB + 80° = 180°

⇒ 2∠OAB = 180° – 80°

⇒ ∠OAB = \(\frac { { 100 }^{ \circ } }{ 2 } \)

⇒ ∠OAB = 50°

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In fig. ∠ACB = 40°, find ∠OAB

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