Event 2: Geometry #1

A "house pentagon" made by stacking an equilateral triangle on top of a square that shares one side. What is the measure of one of the obtuse angles of a house pentagon?
Here is a drawing of some mountains. The tallest peak forms an angle E. What is E? jump -90, -90 pen black rt 90 fd 250 lt 120 label '60°', -> @turnto 0; @slide -25, 10 fd 100 lt 120 label '60°', -> @turnto 0; @slide 0, -30 fd 50 rt 130 label '50°', -> @turnto 0; @slide 5, 30 fd 120 lt 140 label 'E', -> @turnto 0; @slide 0, -30 fd 100 rt 120 label '60°', -> @turnto 0; @slide -5, 30 fd 80 lt 120 label '60°', -> @turnto 0; @slide 5, -30 fd 130 label "#{-90 - bearing()}°", -> @turnto 0; @slide 25, 10 ht()
A spiky nine-pointed star, drawn below, is made of nine segments of equal length, intersecting at equal angles F at each point of the star. What is the measure of the angle F? jump -20, -90 rt 18 pen black for x in [1..9] fd 200 if x is 3 then label 'F', -> @css { fontSize: "8pt" } @turnto 0; @slide 18, -30 rt 160 ht()

1.   ____________ degrees
2.   ____________ degrees
3.   ____________ degrees

Event 2: Geometry #2

Starting from the corner of a rectangular piece of paper, a thin triangle is sliced off. The smallest angle of the removed triangle is five degrees. What angle is left on the other corner of the paper that was sliced (marked with a ?) pen black jump -90, -50 for x in [1..2] fd 100 rt 90 fd 180 rt 90 rt 5 fd 120 ht() label '?', -> @turnto 0; @jump 5, -35
Karla's Kites are shaped as follows, with two right angles on the sides and a seventy degree angle on the bottom. What is the measure of the top angle ? pen black jumpto 0, -90 rt 35 fd 150 lt 90 label '90°', -> @turnto 0; @jump -25, 0 fd 105 jumpto 0, -90 turnto 0 label '70°', -> @jump 0, 25 lt 35 fd 150 rt 90 label '90°', -> @turnto 0; @jump 25, 0 fd 105 label '?', -> @turnto 0; @jump 0, -30 ht()
A regular nine-sided polygon is drawn below, and then sliced in half. What is the angle marked with a "?" ? pen black jump -50, -80 lt 40 for x in [1..9] fd 60 rt 40 fd 30 rt 90 bk 20 fd 210 bk 20 label '?', -> @turnto 0; @jump -20, -3 ht()

1.   ____________ degrees
2.   ____________ degrees
3.   ____________ degrees