21 November
2024
Answer to day before’s geometry puzzle
Triangle ADE is equilateral. Any line parallel to a side of an equilateral triangle forms another equilateral triangle. If you have doubts, think about corresponding angles of a transversal on two parallel lines.
Thus AD = DE.
But DE = DB since sides of square
So triangle ADB is isosceles.
Angle ADB equal 60 degrees plus 90 degrees (equilateral triangle and square) = 150 degrees.
Then angle DBA in the isosceles triangle ADB is 180 degrees minus 150 degrees divided by 2 = 15 degrees.
Angle ABC then is 180 degrees minus the above 15 degrees minus 45 degrees (the lower square diagonal)
= 120 degrees
Pingback: Another geometry puzzle – Rajib Roy
I used trigonometry to get my answer, but this method is simpler.
I have not tried the trig method yet
That’s almost exactly how I got the answer, and we can also find that angle BAE is 45° by the same reasoning
Excellent!