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Math·Geometry and Trigonometry·Lines, angles, and triangles

hard

In the figure, $\overline{WZ}$ and $\overline{XY}$ intersect at point $Q$, $QY=17$, $WX=26$, $QZ=29$, and $QW=34$. The measure of angle $W$ is $a^{\circ }$ and the measure of angle $Y$ is $a^{\circ }$. What is the sum of the perimeters of triangles $QWX$ and $QYZ$?

A

58

B

106

C

118

D

177