Question

look at the diagram of the quilt below.
if the highlighted triangle is rotated clockwise about the center of the quilt, what is the angle of rotation that maps it onto the adjacent triangle?

Explanation:

Step1: Count total equal triangles

Count the number of identical triangles around the center: 8 triangles.

Step2: Calculate full rotation angle

A full rotation around a point is $360^\circ$.

Step3: Find rotation per adjacent triangle

Divide full rotation by number of triangles:
$\frac{360^\circ}{8} = 45^\circ$

Answer:

$45^\circ$