Question

Find the degree measure of the angle subtended at the center of a circle of radius 100 cm by an arc of length 22 cm. (Useπ= 22/7 )//

Answer 1

$\huge{\bf{\underline{\red{Given:}}}}$

Radius of Circle = 100 cm

Length of Arc = 22 cm

$\huge{\bf{\underline{\red{To\:Find:}}}}$

Degree measure of the angle subtended at the centre of a circle.

$\huge{\bf{\underline{\red{Formula\:Used:}}}}$

${\bf{\boxed{r=\dfrac{l}{θ}}}}$

$\huge{\bf{\underline{\red{Solution:}}}}$

Using Formula,

$\sf :\implies\:r=\dfrac{l}{θ}$

Putting Values,

$\sf :\implies\:100=\dfrac{22}{θ}$

$\sf :\implies\:θ=\dfrac{22}{100}$

$\sf :\implies\:θ=\dfrac{11}{50}\: radians$

Now,

$\sf :\implies\:θ=(\dfrac{11}{50}\times \dfrac{180}{\pi})°$

$\sf :\implies\:θ=(\dfrac{11}{5}\times \dfrac{18\times 7}{22})°$

$\sf :\implies\:θ=(\dfrac{11}{5}\times \dfrac{9\times 7}{11})°$

$\sf :\implies\:θ=(\dfrac{693}{55})°$

$\sf :\implies\:θ=(12\dfrac{33}{55})°$

$\sf :\implies\:θ=12°(\dfrac{3}{5}\times 60)'$

$\sf :\implies\:θ=12°36'$

Hence, The Degree measure of the angle subtended at the centre of a circle is 12°36'.

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Answer 2

Answer:

Concept :- use formula

∅ = L/R

Where , ∅ is the angle subtended at the centre of circle.

L is the arc length of the circle.

R is the radius of the circle.

and then use the concept of

C/π = D/180° for radian to degree conversion.

Solution:-

L = 22 cm

R = 100 cm

So, ∅ = 22/100 radian

Now,

D = ( 22/100)×180°/π

= ( 22×180×7/100×22)°

= (63/5)°

= 12° + (3/5)×60'

= 12°36'

Step-by-step explanation:

thanks.