Using a ruler and protractor, construct a rectangle in which one of the diagonals divides the opposite angles into 50° and 40°.

Steps:

1. Draw a line segment AB of any suitable length using a ruler.

2. At B, using protractor, draw ∠ABY = 90°.

3. At A, using protractor, draw ∠BAX = 90°.

4. At A, using protractor, construct ∠BAC = 50° such that AC lies inside the right angle ABY.

5. At A, using protractor, draw ∠CAX = 40° (so that ∠BAC = 50°). The ray AX is perpendicular to AB.

6. From AX, cut off AD = BC using compass (so that AD = BC and ABCD becomes a rectangle).

7. Join CD.

Hence, ABCD is the required rectangle in which diagonal AC divides the opposite angles into 50° and 40°.