BAC =

ABC =

$A  $

$ B $

$ C $

$ M $

What is the measure of $∠BMC$? 

Set angles

solution

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BMC =

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A = (8.38, 6.42)
B = (-1.4, -3.72)
a = Segment(A, B)
abc = 42
bac = 64
inputBox1 = Textfield(bac)
inputBox2 = Textfield(abc)
n: π * abc / 180
m: π * bac / 180
B' = Rotate(B, m, A)
A' = Rotate(A, -n, B)
b = Line(B, A')
c = Line(B', A)
C = Intersect(b, c)
d = AngularBisector(A, B, C)
e = AngularBisector(A, C, B)
f = AngularBisector(C, A, B)
D = Intersect(e, a)
E = Intersect(c, d)
F = Intersect(b, f)
g = Segment(A, C)
h = Segment(B, C)
i = Segment(B, E)
j = Segment(C, D)
k = Segment(F, A)
G = Intersect(i, j)
acb: 180 - abc - bac
abc2: abc / 2
acb2: acb / 2
answer: 180 - acb2 - abc2
text5 = LaTeX(answer, true, true)
text6: "In triangle $ΔABC$, point $M$ is the
point of intersection of the bisectors
of angles $∠BAC$,$ ∠ABC$, and $∠ACB$.
The measure of $∠ABC$ is  " + (LaTeX[abc]) + "°, and
the measure of $∠BAC$ is  " + (LaTeX[bac]) + "°."
α = Angle(C, A, B)
β = Angle(A, B, C)
γ = Angle(G, B, C)
δ = Angle(G, C, B)
ε = Angle(A, C, B)
ζ = Angle(B, G, C)
l = 1 (slider from 1 to 2, step 1)
o = false
text8: "$∠ABC=$ " + (LaTeX[abc]) + "°"
text9: "$∠BAC=$ " + (LaTeX[bac]) + "°"
bmc = 0
inputBox3 = Textfield(bmc)
text11: "$ \frac{" + (LaTeX[acb]) + "°}{2}=" + (LaTeX[acb2]) + "° $"
text10: "$\frac{ " + (LaTeX[abc]) + "°}{2}=" + (LaTeX[abc2]) + " °$"
text12: "$180°-" + (LaTeX[abc]) + "°-" + (LaTeX[bac]) + "°=" + (LaTeX[acb]) + "°$"
text13: "$ 180°-" + (LaTeX[abc2]) + "°-" + (LaTeX[acb2]) + "°=" + (LaTeX[answer]) + "° $"