2019 Fermat Problem 17

The five sides of a regular pentagon are all equal in length. Also, all interior angles of a regular pentagon have the same measure. In the diagram, PQRST is a regular pentagon and \triangle PUT is equilateral. The measure of obtuse \angle QUS is

\textbf{(A)}\ 172^\circ\quad \textbf{(B)}\ 168^\circ\quad \textbf{(C)}\ 170^\circ\quad \textbf{(D)}\ 176^\circ\quad \textbf{(E)}\ 174^\circ

If there are no answer choices shown, enter a numerical answer.

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