A Triangle's Angles

The sum of the measures of the interior angles of any triangle is 180°.

Drag the red point to change the shape of the triangle.
Drag the blue points to rotate the vertices.

Do you see that the interior angles together make a straight angle?
Do you also see how to determine the area of the triangle?

A = (4, 4)
B_1 = (2, 2)
C_1 = (8, 2)
poly1, c, a, b = Polygon(A, B_1, C_1)
d = OrthogonalLine(A, a)
D = Intersect(a, d)
E = Point(Circle[B_1, Distance[A, D]])
e = Segment(B_1, E)
E' = Rotate(E, -Angle[B_1, A, D], B_1)
α = Angle(E', B_1, E)
f = Line(B_1, E')
g = Circle(B_1, Distance[A, B_1])
B = Intersect(g, f, 2)
poly2, e_1, b_1, f_1 = Polygon(B_1, B, E)
h = Line(B_1, d)
k = Circle(B_1, Distance[B_1, E])
G = Intersect(k, h, 1)
i = Line(C_1, d)
p = Circle(C_1, Distance[B_1, E])
H = Intersect(p, i, 1)
I = Point(Circle[C_1, Distance[B_1, E]])
j = Segment(C_1, I)
I' = Rotate(I, Angle[D, A, C_1], C_1)
β = Angle(I, C_1, I')
l = Line(C_1, I')
q = Circle(C_1, Distance[A, C_1])
C = Intersect(q, l, 2)
poly3, j_1, c_1, i_1 = Polygon(C_1, I, C)
m = Segment(G, H)
n = Segment(B_1, G)
r = Segment(C_1, H)
K = Intersect(d, m)
s = Segment(A, K)
poly4, b_2, g_1, h_1, c_2 = Polygon(B_1, G, H, C_1)