Chapter 11.5, Problem 17PPS

To determine

To find the measure of an interior angle of a honeycomb.

Answer to Problem 17PPS

Interior angle of the honeycomb is ${120}^{\circ }$ .

Explanation of Solution

Given:

The individual cells of a honeycomb are hexagons.

Concept used:

The interior angle of a polygon with n sides is $\frac{\left(n-2\right)\times {180}^{\circ }}{n}$ .

Calculation:

Given that the individual cells of a honeycomb are hexagons, which mean that the number of sides is 6.

Therefore interior angle is,

  $\begin{array}{l}\frac{\left(n-2\right)\times {180}^{\circ }}{n}=\frac{\left(6-2\right)\times {180}^{\circ }}{6}\\ =\frac{4\times {180}^{\circ }}{6}\\ =\frac{{720}^{\circ }}{6}\\ ={120}^{\circ }\end{array}$

Hence interior angle of the honeycomb is ${120}^{\circ }$ .