In the given figure- O is the centre of the circle- If -ABD-35- and -BAC-70- find -ACB-

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Angle Subtended by Diameter on the Circle

In the given ...

Question

In the given figure, O is the centre of the circle. If $∠$ ABD=35 $^{\circ}$ and $∠$ BAC=70 $^{\circ}$ , find $∠$ ACB.

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Solution

ANSWER:
It is clear that BD is the diameter of the circle.
Also, we know that the angle in a semicircle is a right angle.
i.e., ∠ BAD = 90 °
Now, considering the Δ BAD, we have:
∠ ADB + ∠ BAD + ∠ ABD = 180 ° (Angle sum property of a triangle)
⇒ ∠ ADB + 90 ° + 35 ° = 180 °
⇒ ∠ ADB = (180 ° - 125 ° ) = 55 °
Angles in the same segment of a circle are equal.
Hence, ∠ ACB = ∠ ADB = 55 °

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In the given figure, O is the centre of the circle. If ∠ABD=35∘ and ∠BAC=70∘, find ∠ACB.

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