Question

in the fig. if angle AOB=40° then, find angle ACB
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Answer 1

Question :

In the figure, if ∠OAB = 40° then, find ∠ACB

Given :

• ∠OAB = 40°

To find :

• ∠ACB

According to the question,

➝ ∠OAB = ∠OBA

➝ ∠OBA = 40°

Reason : Radius of circle.

➝ In △AOB,

➝ ∠OAB + ∠OBA + ∠AOB = 180°

Reason : Angle sum property

➝ 40° + 40° + ∠AOB = 180°

➝ 80° + ∠AOB = 180°

➝ ∠AOB = 180° - 80°

➝ ∠AOB = 100°

So,

• ∠AOB = 100°

➝ ∠ACB = ½ × ∠AOB

➝ ∠ACB = ½ × 100°

➝ ∠ACB = 50°

Reason : Angle subtended by an arc of a circle at the centre is doubled the angle subtended by the same arc at any remaining part of a circle.

• So, ∠ACB = 50°.

Answer 2

$\; \; \; \; \; \; \; \; \;{\Large{\bf{\underbrace{Required \; solution}}}}$

${\large{\bold{\rm{\underline{Question}}}}}$

★ In the figure or attachment , if angle OAB measures 40° then, find angle ACB.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ ABC is given triangle (big)

★ AOB is under form triangle (small)

★ O is centre point

★ In angle OAB measures 40°

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ Angle ACB measures

${\large{\bold{\rm{\underline{Solution}}}}}$

★ Angle ACB measures = 50°

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

☃ According to the figure we can see that,

↝ Angle OAB = 40°

↝ ∠OAB = ∠OBA (Circle's radius)

☃ Now in ∆AOB,

↝ ∠OAB + ∠OBA + ∠AOB = 180° (Angle Sum Property [ASP])

↝ 40° + 40° + ∠AOB = 180° (Angle Sum Property [ASP])

↝ 80° + ∠AOB = 180°

↝ ∠AOB = 180° - 80°

↝ ∠AOB = 100°

☃ Now,

∠ACB = 1/2 × ∠AOB (It's due to the angle arc of the circle)

↝ ∠ACB = 1/2 × 100

↝ ∠ACB = 50°