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In the figure, $AC=CD$. The measure of angle $EBC$ is $45°$, and the measure of angle $ACD$ is $104°$. What is the value of $x$?

In the figure shown, points $Q$, $R$, $S$, and $T$ lie on line segment $PV$, and line segment $RU$ intersects line segment $SX$ at point $W$. The measure of $\angle SQX$ is $48°$, the measure of $\angle SXQ$ is $86°$, the measure of $\angle SWU$ is $85°$, and the measure of $\angle VTU$ is $162°$. What is the measure, in degrees, of $\angle TUR$? 

What is the value of x ?

In the figure, line $m$ is parallel to line $n$. What is the value of $w$?

In the given triangle, and has a measure of . What is the value of x ?

In the figure above, and intersect at point P, , and . What is the measure, in degrees, of ? (Disregard the degree symbol when gridding your answer.)

Right triangles $PQR$ and $STU$ are similar, where $P$ corresponds to $S$. If the measure of angle $Q$ is $18°$, what is the measure of angle $S$?

In the figure, line $q$ is parallel to line $r$, and both lines are intersected by line $s$. If $y=2x+8$, what is the value of $x$?

In the figure above, lines and m are parallel, , and . What is the value of x ?

In the figure above, , , and are parallel. Points B and E lie on and , respectively. If , and , what is the length of , to the nearest tenth?

In triangle $ABC$, the measure of angle $B$ is $90°$ and $\overline{BD}$ is an altitude of the triangle. The length of $\overline{AB}$ is $15$ and the length of $\overline{AC}$ is $23$ greater than the length of $\overline{AB}$. What is the value of $\frac{BC}{BD}$?

In $△XYZ$, the measure of $\angle X$ is $24°$ and the measure of $\angle Y$ is $98°$. What is the measure of $\angle Z$?

Two nearby trees are perpendicular to the ground, which is flat. One of these trees is $10$ feet tall and has a shadow that is $5$ feet long. At the same time, the shadow of the other tree is $2$ feet long. How tall, in feet, is the other tree?

In the figure, line $m$ is parallel to line $n$. What is the value of $w$?

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

In triangles $LMN$ and $RST$, angles $L$ and $R$ each have measure $60°$, $LN=10$, and $RT=30$. Which additional piece of information is sufficient to prove that triangle $LMN$ is similar to triangle $RST$?

Triangles ABC and DEF are shown above. Which of the following is equal to the ratio ?

In the figure above, what is the length of ?

Triangle $XYZ$ is similar to triangle $RST$ such that $X$, $Y$, and $Z$ correspond to $R$, $S$, and $T$, respectively. The measure of $\angle Z$ is $20°$ and $2XY=RS$. What is the measure of $\angle T$?

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?

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.)

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 $P^{\text{'}}$?