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Math·Geometry and Trigonometry·Right triangles and trigonometry

hard

For two acute angles, $\angle Q$ and $\angle R$, $\cos (Q)=\sin (R)$. The measures, in degrees, of $\angle Q$ and $\angle R$ are $x+61$ and $4x+4$, respectively. What is the value of $x$?

A

$5$

B

$19$

C

$23$

D

$29$