Remember that the sum of the interior angles of a triangle is always 180°. We can take advantage of that fact to find the remaining angle in triangle PQR and triangle RST:
For triangle PQR:
[tex] \alpha =180-(100+66)[/tex]
[tex] \alpha =180-166[/tex]
[tex] \alpha =14[/tex]
For triangle RST:
[tex] \beta =180-(14+100)[/tex]
[tex] \beta =180-114[/tex]
[tex] \beta =66[/tex]
Since both triangles have interior angles 100°, 66°, and 14°, we can conclude that the triangles are similar.
