In the given figure, if ∠ = 40 , then find the measure of ∠
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Step-by-step explanation:
In ΔOAB, we have
OA=OB .....(radii of the same circle).
∴ΔOAB is isosceles.
∴∠OAB=∠OBA⇒∠OAB+∠OBA=2∠OAB
So, ∠AOB+∠OAB+∠OBA=∠AOB+2∠OAB=180
o
....(angle sum property of triangles).
∴∠OAB=
2
1
(180
o
−∠AOB) ..........(i)
Now ∠AOB=2∠ACB=2×40
o
=80
o
....(The angle subtended by a chord of a circle at the centre is double of that at the cicumference)
From (i), we have
∠OAB=
2
1
(180
o
−80
o
)=50
o
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