Let's say Angela's weekly allowance is x.
She spent half of her weekly allowance at the movies, which is 0.5x.
After the movie, she has 0.5x left.
Her parents let her clean the windows and earn $5, so her total money at the end of the week is 0.5x + 5.
According to the given information, she ended the week with $8, so we have the equation:
0.5x + 5 = 8
Subtracting 5 from both sides of the equation, we get:
0.5x = 3
Dividing both sides of the equation by 0.5, we get:
x = 6
Therefore, Angela's weekly allowance is $6.