Answer:
[tex]\begin{gathered}\large\qquad\qquad\boxed{ \bold{ \: \: \:( A ) \: \: \: 15 \: \: \: }} \\ \end{gathered} [/tex]
Step-by-step explanation:
Given that, exterior angle of a regular polygon is 24°.
We have to find the number of sides of a regular polygon.
We know,
Exterior angle and number of sides (n) of regular polygon are connected by the relationship
[tex]\begin{gathered}\qquad \leadsto \: \boxed{ \sf{ \: \:n = \dfrac{360\degree}{Exterior \: angle} \: \: }} \\ \end{gathered} [/tex]
[tex] \sf{ \pmb{So}, \: on \: \pmb{substituting }\: the \: \pmb{value}, \: we \: \pmb{ get} : } \\ [/tex]
[tex]\begin{gathered}\qquad \implies \: \sf{ \:n = \dfrac{360\degree}{24\degree} \: } \\ \end{gathered} [/tex]
[tex]\begin{gathered}\qquad\sf\implies \: \sf{ \:n =15 \: } \\ \end{gathered} [/tex]
[tex] \large \sf{ \pmb{Hence,}} \\ [/tex]
[tex]\begin{gathered}\sf\qquad \mapsto \: \underline{\bold{Number\:of\:sides}} \: \bold{ = \: \pmb{ 15}} \\ \end{gathered} [/tex]
[tex] \\ [/tex]
[tex] \qquad \qquad \large \underline{ \sf{ \blue{Additional \: Information : }}} \\ [/tex]
Sum of all interior angles of a convex polygon of n sides is:
[tex]\begin{gathered}\sf \:\qquad \mapsto \: \boxed{ \sf{ \: \:(2n - 4) \times 90\degree \: \: }} \\ \end{gathered} [/tex]
For a regular polygon of n sides, we have a relationship:
[tex]\begin{gathered}\qquad \mapsto \: \boxed{ \sf{ \: \:Exterior \: angle \: = \: \frac{360\degree}{n} \: \: }} \\ \end{gathered} [/tex]
[tex]\begin{gathered}\qquad \mapsto \: \boxed{ \sf{ \: \:n \: = \: \frac{360\degree}{Exterior \: angle} \: \: }} \\ \end{gathered} [/tex]
The smallest interior angle of a regular polygon is 60°.
The largest exterior angle of a regular polygon is 120°.