Question

find the degree measures of the angle subtended at the centre of a circle of radius 100cm by an arc of length 22 cm.

Answer 1

$100 \times 22 \div 7 \times 2$
this is the circumference.which can be written as 100×3.14×2=314×2=628cm.
now 22/628=a/360
628a=22×360
a=22×360/628
a=11×180/157=12.6 or 13(approx)

Answer 2

Step-by-step explanation:

$\bullet\:\:\textsf{Radius = (r) = \textbf{100 cm}}$

$\bullet\:\:\textsf{Arc Length = (l) = \textbf{22 cm}}$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$\qquad \tiny \dag \: \underline {\bf Formula \: used :}$

$\bigstar \: \: \sf l = r \: \theta \: \: \bigstar$

$\qquad \tiny \dag \: \underline {\bf Putting \: the \: value :}$

$: \implies \sf 22 = 100 \times \theta$

$: \implies \underline{ \boxed{\sf \theta = \dfrac{22}{100} \: radians}}$

____________________

$\qquad \tiny \dag \: \purple{\underline {\bf We \: need \: to \: find \: \theta \: into \: degree:}}$

$\dashrightarrow\:\:\sf Radian \: measure = \dfrac{\pi}{180} \times Degree \: measure \\ \\ </p><p>$

$\dashrightarrow\:\:\sf \dfrac{22}{100} = \dfrac{22}{180} \times \dfrac{1}{7} \times Degree \: measure \\ \\ </p><p>$

$\dashrightarrow\:\:\sf \dfrac{22}{100} \times \dfrac{180}{22} \times \dfrac{7}{1} = Degree \: measure$

$\dashrightarrow\:\: \sf Degree \: measure = \frac{126}{10}$

$\dashrightarrow\:\: \sf Degree \: measure = 12.6^{\circ}$

$\dashrightarrow\:\: \sf Degree \: measure = 12^{ \circ} + 6^{\circ}$

$\dashrightarrow\:\: \sf Degree \: measure = 12^{\circ} + (0.6 \times 60)$

$\dashrightarrow\:\: \underline{ \boxed{ \sf Degree \: measure = 12^{\circ} \: 36'}}$