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Point $O$ is the center of a circle. The measure of arc $RS$ on this circle is $100°$. What is the measure, in degrees, of its associated angle $ROS$?

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?

A circle has a circumference of $31\pi$ centimeters. What is the diameter, in centimeters, of the circle?

The equation defines a circle in the xy‑plane. What is the radius of the circle?

Triangle $ABC$ is similar to triangle $XYZ$, such that $A$, $B$, and $C$ correspond to $X$, $Y$, and $Z$ respectively. The length of each side of triangle $XYZ$ is $2$ times the length of its corresponding side in triangle $ABC$. The measure of side $AB$ is $16$. What is the measure of side $XY$?

In $△XYZ$, the measure of $\angle X$ is $23°$ and the measure of $\angle Y$ is $66°$. What is the measure of $\angle Z$?

In the figure, line $m$ is parallel to line $n$, and line $t$ intersects both lines. What is the value of $x$? 

In triangle $JKL$, the measures of $\angle K$ and $\angle L$ are each $48°$. What is the measure of $\angle J$, in degrees? (Disregard the degree symbol when entering your answer.)

A circle in the xy-plane has its center at $\left(-4,-6\right)$. Line $k$ is tangent to this circle at the point $\left(-7,-7\right)$. What is the slope of line $k$?

A manufacturer determined that right cylindrical containers with a height that is 4 inches longer than the radius offer the optimal number of containers to be displayed on a shelf. Which of the following expresses the volume, V, in cubic inches, of such containers, where r is the radius, in inches?

In the figure above, . If and , what is the length of ?

Quadrilateral $P^{\text{'}}{Q}^{\text{'}}{R}^{\text{'}}{S}^{\text{'}}$ is similar to quadrilateral $PQRS$, where $P$, $Q$, $R$, and $S$ correspond to $P^{\text{'}}$, $Q^{\text{'}}$, $R^{\text{'}}$, and $S^{\text{'}}$, respectively. The measure of angle $P$ is $30°$, the measure of angle $Q$ is $50°$, and the measure of angle $R$ is $70°$. The length of each side of $P^{\text{'}}{Q}^{\text{'}}{R}^{\text{'}}{S}^{\text{'}}$ is $3$ times the length of each corresponding side of $PQRS$. What is the measure of angle $P^{\text{'}}$?

The number of radians in a 720-degree angle can be written as , where a is a constant. What is the value of a ?

At a certain time and day, the Washington Monument in Washington, DC, casts a shadow that is 300 feet long. At the same time, a nearby cherry tree casts a shadow that is 16 feet long. Given that the Washington Monument is approximately 555 feet tall, which of the following is closest to the height, in feet, of the cherry tree?

In the figure above, intersects at C. If , what is the value of y ?

For the triangle shown, which expression represents the value of $a$?

In triangle ABC, the measure of angle A is . If triangle ABC is isosceles, which of the following is NOT a possible measure of angle B ?

In the figure above, . What is the value of x ?

In the figure, lines $m$ and $n$ are parallel. If $x=6k+13$ and $y=8k-29$, what is the value of $z$?

An isosceles right triangle has a hypotenuse of length $58$ inches. What is the perimeter, in inches, of this triangle?

A circle has center $O$, and points $R$ and $S$ lie on the circle. In triangle $ORS$, the measure of $\angle ROS$ is $88°$. What is the measure of $\angle RSO$, in degrees? (Disregard the degree symbol when entering your answer.)

Triangle ABC and triangle DEF are similar triangles, where and are corresponding sides. If and the perimeter of triangle ABC is 20, what is the perimeter of triangle DEF ?

In the xy-plane, the graph of is a circle. What is the radius of the circle?

An isosceles right triangle has a perimeter of $94+94\sqrt{2}$ inches. What is the length, in inches, of one leg of this triangle?

$RS=440$

$ST=384$

$TR=584$

The side lengths of right triangle $RST$ are given. Triangle $RST$  is similar to triangle $UVW$, where $S$ corresponds to $V$ and $T$ corresponds to $W$. What is the value of $\tan W$?