For The Mathematically Inclined

An architect wants to design a stairway with a total rise of 9 feet, a riser height between 7 and 8 inches, and an odd number of steps. How many steps did he have in the stairway?

In Fig. 1 on right, the regular pentagon GHIJK is constructed inside a regular octagon ABCDEFGH so that the two polygons share side GH. If the line segments BC and IJ are extended so that they meet at point X, how many degrees are there in the measure of angle BXI?

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Problems for 10/12/23

Problem 1

60⁴⁰
--- = ?
30²⁰

Problem 2

x² + y² = 61, xy = 30. What is x+y?