Angles in rectangles and squares

A B C D is a rectangle, lettered clockwise from the top left. The line B P is drawn from B to a point P on D C. Angle A B P equals 31 degrees. Find angle P B C. Try it first. Pause if you like. Which complete corner contains both the given angle and the angle we need? Angle A B C equals 90 degrees. B is a corner of the rectangle. Follow the whole turn from B A to B C. The 31-degree angle is between B A and B P. The middle letter B names the vertex. Angle P B C equals 90 degrees minus 31 degrees. It is the part between B P and B C. That equals 59 degrees. The two parts fit inside the same right angle. Look at the small rectangle. Each corner has a square mark. All four corners are right angles. The square also has a square mark at every corner. It has four right angles too.

E F G H is a rectangle, lettered clockwise from the top left. Two lines H J and H K are drawn from H to the points J and K on E F. Angle E H J equals 26 degrees and angle K H G equals 18 degrees. Find angle J H K. Try it first. Pause if you like. The unknown is between the two lines. How many given parts share its right angle? Angle E H G equals 90 degrees. This is the rectangle corner at H, from H E to H G. The 26-degree part lies between H E and H J. The 18-degree part lies between H K and H G. Both given parts belong to this corner. Angle J H K equals 90 degrees minus 26 degrees minus 18 degrees. Subtract both given parts in one line. That equals 46 degrees. The middle angle J H K is 46 degrees. Name the right angle first. Subtract every given part inside it.