Question

Find the ratio between the exterior angles of a regular hexagon and regular pentagon.

• A. 6: 5
• B. 5: 6
• C. 7: 5
• D. 5: 7

Answer 1

The correct option is B

5: 6

Number of sides in a hexagon is '6' and in a pentagon is '5'.

A regular polygon is a polygon in which all sides and all angles are equal. Since given that the pentagon and hexagon are regular so all the angles in that respective polygons will be equal.

Let the exterior angle in regular pentagon be $x^{\circ }$ and regular hexagon be $y^{\circ }$.

$\because$ Sum of exterior angles is ${360}^{\circ }$

$\Rightarrow$ 5$x^{\circ }$ = ${360}^{\circ }$ (for regular pentagon) and 6$y^{\circ }$ = ${360}^{\circ }$ (for regular hexagon)

$\Rightarrow$ $x$ = $\frac{360}{5}$ and $y$ = $\frac{360}{6}$

$\Rightarrow$ $x$ = ${72}^{\circ }$ and $y$ = ${60}^{\circ }$

$\therefore$ ratio of exterior angles of a regular hexagon and regular pentagon = $y$ : $x$

= 60 : 72

= 5: 6