Question 16

The length of a minor are is $$\frac{2}{9}$$ of the circumference of the circle. Write the measure of the angle (in degrees) subtended by the are at the centre of the circle.

Solution

According to the question

Length of minor arc = $$\frac{2}{9}$$ of circumference of the circle

we know that,

Lenght of arc = $$theta\div 360\times 2πr$$

circumference of circle = 2πr

Apply in the question

$$theta\div 360\times 2 π r = \frac{2}{9}\times 2πr$$

$$theta\div 360 = \frac{2}{9}$$

theta = $$\frac{2}{9}\times 360$$

theta = 80.

So, the measure of angle subtended is 80°.

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