Question

a regular octagon is shown below. suppose that the octagon is rotated counter - clockwise about its center so that the vertex at t is moved to y. how many degrees does the octagon rotate?

Explanation:

Step1: Find central - angle of regular octagon

The sum of central - angles around a point is $360^{\circ}$. For a regular octagon, the central - angle between consecutive vertices is $\frac{360^{\circ}}{8}=45^{\circ}$.

Step2: Count number of vertices between T and Y

Counting the vertices from T to Y in the counter - clockwise direction, there are 3 vertices between them.

Step3: Calculate rotation angle

Since the central - angle between consecutive vertices is $45^{\circ}$, and there are 3 intervals from T to Y, the rotation angle is $45^{\circ}\times3 = 135^{\circ}$.

Answer:

$135$