Problem 267

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Opposite angles are equal in measure and so $t=50\degree$ since it is opposite the angle whose measure is given as $50\degree$. By a property of parallel lines, the angles whose measures are $t$ and $x$ form a "C pattern", and are supplementary. Thus $t+x=180\degree$ or $x=180\degree-50\degree=130\degree$. Since the angle whose measure is $y$ is opposite the angle whose measure is $x$, then $y=x=130\degree$. Since $t+y=50\degree+130\degree=180\degree$, then from the given answers, $t$ and $y$ are the pair of angles whose measures sum to $180\degree$. Of the answers given, we confirm that no other pair of angles have measures whose sum is $180\degree$ by
determining the measures of each of the missing angles, as shown.