Question

The figure shows a 10 x 10 square centered at the origin. The darker shaded square is the image of this square, dilated by a factor of 0.8 and rotated about the origin by exactly the number of degrees, theta, so that its corners touch the sides of the parent square. The corners of the rotated square divide the sides of the 10 x 10 squade into segments of length a and b. Use the fact that a and b add up to 10 to find the value of theta.