Question

In each of the following figure, O is the centre of the circle. Find the measure of each lettered angle.​

Answer 1

Given, in the following figure, O is the centre of the circle, ∠BAC is 63° and ∠BCA is x .

In ∆ABC,

∠BAC = 63°

∠ABC = 90° (Angle in a semi-circle is 90°)

∠BCA = x

By using the angle sum property of a triangle, we get

∠BAC + ∠ABC + ∠BCA = 180°

By putting the respected values, we get

63° + 90° + x = 180°

or, 123° + x = 180°

By transposition method, we get

or, x = 180° - 123°

or, x = 57°

Answer:

The value of x is 57° .

Answer 2

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Given, in the following figure, O is the centre of the circle, ∠BAC is 63° and ∠BCA is x .

In ∆ABC,

∠BAC = 63°

∠ABC = 90° (Angle in a semi-circle is 90°)

∠BCA = x

By using the angle sum property of a triangle, we get

∠BAC + ∠ABC + ∠BCA = 180°

By putting the respected values, we get

63° + 90° + x = 180°

or, 123° + x = 180°

By transposition method, we get

or, x = 180° - 123°

or, x = 57°