MathDB

[asy] import cse5; size(180); pathpen=black; pair A1=(0,0), A2=(1,0), A3=(0.5,sqrt(3)/2); D(MP("A_1",A1)--MP("A_2",A2)--MP("A_3",A3,N)--cycle); pair A4=(A1+A2)/2, A5 = (A3+A2)/2, A6 = (A4+A3)/2; D(MP("A_4",A4,S)--MP("A_6",A6,W)--A3); D(A6--MP("A_5",A5,NE)--A4); //Credit to chezbgone2 for the diagram[/asy]
If

\triangle A_1A_2A_3

is equilateral and

A_{n+3}

is the midpoint of line segment

A_nA_{n+1}

for all positive integers

n

, then the measure of

\measuredangle A_{44}A_{45}A_{43}

equals

<span class='latex-bold'>(A) </span>30^\circ\qquad<span class='latex-bold'>(B) </span>45^\circ\qquad<span class='latex-bold'>(C) </span>60^\circ\qquad<span class='latex-bold'>(D) </span>90^\circ\qquad <span class='latex-bold'>(E) </span>120^\circ

Problem Statement