The difference between two adjacent angles is 90 °. Find the magnitude of these angles?

Adjacent angles are known to always add up to 180 °.

By condition, their difference is 90 °, which means that one of the angles is 90 ° larger than the other.

Let the smaller angle be x °, then the larger angle is (x + 90) °.

Let’s make the equation:

x + (x + 90) = 180;

x + x + 90 = 180;

2x + 90 = 180;

2x = 180 – 90;

2x = 90;

x = 90: 2;

x = 45 °.

This is the smaller angle. There are two possibilities to find the second one:

1) 180 ° – 45 ° = 135 °,

2) 45 ° + 90 ° = 135 °.

Answer: 45 ° and 135 °.