Question

The diagram shows 2 congruent regular polygons joined together. Work out the number of sides of each polygon. The exterior angles equal to 72°.

Answer 1

Answer: There are five sides in a polygon.

Step-by-step explanation:

Since we have given that

Measure of exterior angles = 72°

We need to find the number of sides of  polygon.

As we know the formula for "Number of sides of polygon".

Number of sides is given by

$\frac{360^\circ}{72^\circ}\\\\=5$

Hence, there are five sides in a polygon.

Answer 2

The number of sides of each polygon whose exterior angles equal to 72° is 5 and this can be determined by using the formula of number of sides of a polygon when the exterior angle is given.

Given :

2 congruent regular polygons joined together.

The polygon is a closed structure made of straight lines and it is a two-dimensional structure.

The formula for finding the total number of sides a polygon has is given by:

$\rm S = (n - 2)\times 180^\circ$

where 'n' is the total number of sides and 'S' is the sum of interior angles.

Now, if the exterior angle is given then the formula of number of sides of a polygon is given by:

$\rm n = \dfrac{360^\circ}{exterior \;angle}$

Now, put the value of the exterior angle in the above equation.

$n = \dfrac{360^\circ}{72^\circ}$

n = 5

The number of sides of each polygon whose exterior angles equal to 72° is 5.

For more information, refer to the link given below:

https://brainly.com/question/2096984