Question

Use the slider to rotate pentagon ABCDE about the center of rotation, R. The angle through which the pentagon is rotated is , represented by the variable , where . At what values of does pentagon coincide with pentagon ? Enter the values in the table. For each value of α that you enter, enter the vertex that coincides with vertex .

Answer 1

Answer:

α C′

72° B

144° A

216° E

288° D

360° C

Step-by-step explanation:

Answer 2

When a shape is rotated, the shape is turned about a center. The angles that pentagon ABCDE will coincide with itself when rotated are: $72^o, 144^o, 216^o, 288^o$ or $360^o$

A pentagon has

$n = 5$ --- number of sides

$\theta = 360^o$ --- total angles

For pentagon ABCDE to rotate and coincide with itself, the angle of rotation must be:

$\alpha = \frac{\theta}{n}$

So, we have:

$\alpha = \frac{360^o}{5}$

$\alpha = 72^o$

Other angles of rotation must be a multiple of $72^o$

So, we have:

$\alpha = 72^o, 144^o, 216^o, 288^o,360^o$

Hence, pentagon ABCDE must rotate at any of: $72^o, 144^o, 216^o, 288^o$ or $360^o$ to coincide with itself.

The points of coincidence are:

$72^o \to A$

$144^o \to B$

$216^o \to C$

$288^o \to D$

$360^o \to E$

See attachment for first rotation at $72^o$

Read more about rotations at:

https://brainly.com/question/1571997