The angle made by an arc at the centre of the circle is double the angle made by the same arc at any point on the circle. The measure of the angle θ will be 45°.
What are an arc and subtended angle theorem?
According to the arc and subtended angle theorem, The angle made by an arc at the centre of the circle is double the angle made by the same arc at any point on the circle.
The angle made by an arc at the centre of the circle is double the angle made by the same arc at any point on the circle. Therefore, the measure of the angle θ will be half the measure of the ∠P.
As it can be observed the measure of the angle ∠P is 90°, therefore, the measure of the angle θ can be written as,
∠P = 2 × ∠θ
90° = 2 × ∠θ
∠θ = 45°
Hence, the measure of the angle θ will be 45°.
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