Question

the length of a minor arc is 2/9 of the circumference of the circle. write the measure of the angle subtended by the arc at the centre of the circle.

Answer 1

According to the question

Length of minor arc = 2/9 of circumference of the circle

we know that,

Lenght of arc = theta/360 * 2πr

circumference of circle = 2πr

Apply in the question

theta/360 *2 π r = 2/9 * 2 πr

theta/360 = 2/9

theta = 2/9 * 360

theta = 80.

So, the measure of angle subtended is 80°.

Answer 2

The measure of the angle subtended by the arc at the centre of the circle is 80°.

Given:

The length of a minor arc = $\frac{2}{9}$ of the circumference of the circle

To find:

The measure of the angle subtended by the arc at the centre of the circle

Formula used :

Circumference of the circle = 2πr

Length of minor arc = $2 \pi r \times \frac{\theta}{360 \°}$

Solution:

Step1: Find the measure of the angle subtended by the arc at the centre of the circle:

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

$2 \pi \times r \times \frac{\theta}{360 \°} = \frac{2}{9} \times 2 \pi \times r \\\\\frac{\theta}{360 \°} = \frac{2}{9} \\\\\theta = \frac{2}{9} \times 360 \°$

$\theta = 2 \times 40 \°$

$\theta$ = 80°

Hence, the measure of the angle subtended by the arc at the centre of the circle is 80°.

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