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

hard

- Triangle $WXQ$ has a common vertex with triangle $YZQ$.
- The common vertex is $Q$.
- For triangle $WXQ$:
- The measure of angle $W$ is $a^{\circ }$.
- For triangle $YZQ$:
- The measure of angle $Y$ is $a^{\circ }$.

In the figure, $WZ$ and $XY$ intersect at point $Q$, $QY=17$, $WX=26$, $QZ=29$, and $QW=34$.
What is the sum of the perimeters of triangles $QWX$ and $QYZ$?

A

58

B

106

C

118

D

177