SAT Math: Geometry and Trigonometry

In the figure shown, lines $r$ and $s$ are parallel, and line $m$ intersects both lines. If $y < 65$, which of the following must be true?


Note: Figure not drawn to scale.

What is the value of $\tan \frac{92 \pi}{3}$?

The circle shown has center $O$, circumference $144\pi$, and diameters $\overline{PR}$ and $\overline{QS}$. The length of arc $\stackrel{\frown}{PS}$ is twice the length of arc $\stackrel{\frown}{PQ}$. What is the length of arc $\stackrel{\frown}{QR}$?

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In the figure, two lines intersect at a point. If $w = 136$, what is the value of $z$?

The side length of a square is $55$ centimeters $(\text{cm})$. What is the area, in $\text{cm}^2$, of the square?

In triangles $ABC$ and $DEF$, angles $B$ and $E$ each have measure $27^{\circ}$ and angles $C$ and $F$ each have measure $41^{\circ}$. Which additional piece of information is sufficient to determine whether triangle $ABC$ is congruent to triangle $DEF$?

In triangle $ABC$, angle $B$ is a right angle. The length of side $AB$ is $10\sqrt{37}$ and the length of side $BC$ is $24\sqrt{37}$. What is the length of side $AC$?

In $\triangle RST$, the measure of $\angle R$ is $63^{\circ}$. Which of the following could be the measure, in degrees, of $\angle S$?