$\bold\textsf{P}$

\textsf{Slide to explore}

$\text{NEW FIGURE}$

\text{Angle Measurements}

slideToExplore = 0 (slider from 0 to 2, step 0.01)
I = (-1.7320508075688772, -1)
J = (-1.7320508075688772, -3)
K = (1.7320508075688772, -3)
pol1V: {I, J, K}
L = (-3.4641016151377544, -1)
M = (-0.8660254037844386, 0.5)
N = (-2.598076211353316, 1.5)
O = Point(xAxis)
pol2V: {L, M, N, O}
P = (-5.196152422706631, -3)
Q = (-2.598076211353315, -1.5)
R = (-7.794228634059947, 1.5)
S = (-5.196152422706631, 3)
pol3V: {Q, R, S, P}
T = (-2.598076211353316, 0.5)
U = (-5.196152422706632, -1)
V = (-7.794228634059947, 0.5)
pol4V: {T, V, U}
case = 1 (slider from 1 to 5, step 1)
W = (-1.7320508075688772, -2)
Z = (0, -1)
A_1 = (0, -3)
B_1 = (1.7320508075688772, -2)
C_1 = (1.7320508075688772, 1)
D_1 = (0.8660254037844386, 0.5)
E_1 = (0.8660254037844386, 1.5)
F_1 = (-1.7320508075688772, 0)
pol5V: {F_1, W, Z, A_1, B_1, C_1, D_1, E_1}
polV = Element({pol1V, pol2V, pol3V, pol4V, pol5V}, case)
numOfSides = Length(polV)
num: floor((numOfSides * Max[0, slideToExplore - 1]))
sides = Zip(Segment[AA, BB], AA, polV, BB, Append[Take[polV, 2, Length[polV]], polV(1)])
v4: (0, -4)
v3: (-8, 0)
v2: (0, 5)
v1: (6, 0)
vec = Element({v1, v2, v3, v4}, case)
poly1 = Polygon(polV)
AppSize = Corner(5)
MoveGuideLine = (3.7788168584374993, 4.49655119296)
hGuideline: y = y(MoveGuideLine)
vGuideline: x = x(MoveGuideLine)
ViewCorner1_{1} = (-7.71925, -3.45376)
ViewCorner3_{1} = (3.7694, 4.47784)
q1_{1} = Polygon({ViewCorner1_{1}, (x(ViewCorner3_{1}), y(ViewCorner1_{1})), ViewCorner3_{1}, (x(ViewCorner1_{1}), y(ViewCorner3_{1}))})
xAxisFake_{1} = Segment((x(ViewCorner1_{1}), 0), (x(ViewCorner3_{1}), 0))
text1_{1} = Text("x", (x(ViewCorner3_{1}) - x(ViewCorner3_{1} - ViewCorner1_{1}) / 20, 0), true, true, 0, 1)
text2_{1} = Text("y", (0, y(ViewCorner3_{1}) - y(ViewCorner3_{1} - ViewCorner1_{1}) / 20), true, true, 1, 0)
Cor1 = (-8.0400750625, -5.1401201599999995)
Cor3 = (8.040049999999999, 4.94008)
yAxisFake_{1} = Segment((0, y(ViewCorner1_{1})), (0, y(ViewCorner3_{1})))
eq1: x = x(Corner[1]) + (x(Corner[2] - Corner[1]) / 800 * 16)
eq2: x = x(Corner[2]) - (x(Corner[2] - Corner[1]) / 800 * 16)
A: polV(1)
B: (-6, 1)
C = (-5, 1)
D = (-5, -1)
E = (-4, -1)
F = (-4, 2)
G = (-5, 2)
H = (-5, 3)
dist: 6
B' = Translate(B, Vector[A, A + (dist * (Min[slideToExplore, 1], 0))])
C' = Translate(C, Vector[A, A + (dist * (Min[slideToExplore, 1], 0))])
D' = Translate(D, Vector[A, A + (dist * (Min[slideToExplore, 1], 0))])
E' = Translate(E, Vector[A, A + (dist * (Min[slideToExplore, 1], 0))])
F' = Translate(F, Vector[A, A + (dist * (Min[slideToExplore, 1], 0))])
G' = Translate(G, Vector[A, A + (dist * (Min[slideToExplore, 1], 0))])
H' = Translate(H, Vector[A, A + (dist * (Min[slideToExplore, 1], 0))])
angRotate = Element({120°, 180°, 60°, 180°, 180°}, case)
poly1' = Rotate(poly1, ((Min[slideToExplore, 1] * angRotate) * If[case ≥ 3, -1, 1]), A)
colorHighl: {0, 168, 60} / 255
a: ((slideToExplore - 1) * 5) + 0.5
hGuideline' = Translate(hGuideline, Vector[(Vector[Corner[1], Corner[4]] / 500 * 16)])
sides' = Rotate(sides, (Min[1, slideToExplore] * 90°), A)
l1: {InteriorAngles[poly1]}
l3: {InteriorAngles[poly1]}
angs = First(l1, num)
sidesToShowAlt: {"120°", "60°", "300°", "60°", "120°", "60°", "300°", "60°"}
sidesToShow = Take(If[case ≟ 5, sidesToShowAlt, Zip[Text[tt], tt, l1]], 1, Max[1, ((slideToExplore - 1) * Length[sides])])
sidesToShow' = Take(angs, 1, Max[1, ((slideToExplore - 1) * Length[sides])])
horiz1: {2, 3, -4}
vert1: {-3, 2, 1}
horiz2: {1, -3.5, 0, 4}
vert2: {3.5, 0, -3.5, 0}
horiz3: {-3.5, 4, -1.5, 2}
vert3: {0, 0, -3, 4}
horiz4: {-4.5, 4.5, -1}
vert4: {-0.9, -0.9, 3.5}
vert5: {0, 3, 1.5, 3, 3, 1, -0.5, 1}
vert = Element({vert1, vert2, vert3, vert4, vert5}, case)
horiz5: {4, 2, 0, 2, -2, 0, 0, 0}
horiz = Element({horiz1, horiz2, horiz3, horiz4, horiz5}, case)
labelsPos = Zip(AA + (0.25 * (hh, vv)), AA, polV, hh, horiz, vv, vert)
angsLabels = Zip(Text[(("\textsf{" * kk) * "}"), AA, true, true, 0, 0], kk, sidesToShow, AA, labelsPos)
labelsPos' = Rotate(labelsPos, (angRotate * If[case ≥ 3, -1, 1]), A)
vGuideline' = Translate(vGuideline, Vector[(Vector[Corner[1], Corner[2]] / 800 * 32)])
poly1Black: poly1
poly1Black': poly1'
polV' = Rotate(polV, 90°, A)
tabOrder: {slideToExplore, btnNew}
l2: {InteriorAngles[poly1']}
angs' = First(l2, num)
l4: {InteriorAngles[poly1']}
angsLabels' = Zip(Text[(("\textsf{" * kk) * "}"), AA, true, true, 0, 0], kk, sidesToShow, AA, labelsPos')
table = TableText(Zip[Text[(("\textsf{" * kk) * "}")], kk, sidesToShow], Zip[Text[(("\textsf{" * kk) * "}")], kk, sidesToShow], "c_|v", 90)