Find adjacent angles if the difference is 90 °.

Let’s denote by x the smaller of the given adjacent angles, and by y – the larger of the given adjacent angles.

According to the condition of the problem, the difference between these angles is 90 °, therefore, we can write the following relationship:

y – x = 90.

Since the adjacent angles add up to the unfolded angle, we can write the following relationship:

y + x = 180.

We solve the resulting system of equations.

Adding the first equation with the second, we get:

y – x + y + x = 90 + 180;

2y = 270;

y = 270/2;

y = 135 °.

Knowing the larger angle, we find the smaller one:

x = 180 – y = 180 – 135 = 45 °.

Answer: Adjacent angles are 135 ° and 45 °.