Question

what is the angle subtended at the centre of a circle of radius 5cm by an arc length 4pie cm​

Answer 1

144° is the answer .

Solution in attachment

Answer 2

The angle subtended at the center of a circle is equals to 144 degrees.

Step-by-step explanation:

In the given question we need to find the value of angle subtended at the center of a circle.

For reference, an image of the problem has been attached.

Given that radius of the circule is 5 cm, arc length is 4$\pi$ cm.

Let Angle be denoted by Ф

Let Radius be denoted by r and arc length by l i.e.

r=5cm and l=4$\pi$ cm

Now to find the angle, we have  Ф=l/r--------(1) where  Ф is in radians.

To convert radians into degree, we use the following formula.

i.e.  (Ф)radians =  ($\pi$/180) *(Ф)degree---------(2)

⇒ From eq(1) , we have

Ф= 4$\pi$/5 radians

from eq(2), we have

⇒Ф= (4$\pi$/5)*(180/$\pi$  )

⇒Ф=144⁰

Hence the angle subtended at the centre of a circle is 144⁰.

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