Question

Match the angle subtended by an arc of given length , if the circumference of a circle is 512 cm.

• A. ${180}^{\circ }$
• B. ${22.5}^{\circ }$
• C. ${56.25}^{\circ }$

Answer 1

Arc length $=\frac{\text{angle subtended}}{{360}^{\circ }}\times \text{Circumference of the circle}$

$\Rightarrow$ Angle subtended $=\frac{\text{Arc length}}{\text{Circumference of the circle}}\times {360}^{\circ }$

When arc length =216 cm,

$\Rightarrow$ Angle subtended $=\frac{216}{512}\times {360}^{\circ }={180}^{\circ }$

When arc length = 32 cm,

$\Rightarrow$ Angle subtended $=\frac{32}{512}\times {360}^{\circ }={22.5}^{\circ }$

When arc length = 80 cm,

$\Rightarrow$ Angle subtended $=\frac{80}{512}\times {360}^{\circ }={56.25}^{\circ }$