Lines, Angles, and Triangles 1 — Geometry and Trigonometry

Questions in this quiz (10)

1. What is the value of $$x$$?

   • $$20^\circ$$
   • $$35^\circ$$
   • $$115^\circ$$
   • $$135^\circ$$

2. If $$BD=8$$ and $$AD=4$$, what is the length of $$DC$$?

   • $$12$$
   • $$16$$
   • $$20$$
   • $$24$$

3. What is the length of $$BD$$?

   • $$12$$
   • $$\frac{53}{4}$$
   • $$\frac{336}{25}$$
   • $$15$$

4. Two right triangles are shown. In triangle $$ABC$$, $$\angle B=90^\circ$$ and $$\angle C=55^\circ$$. In triangle $$DEF$$, $$\angle E=90^\circ$$ and $$\angle F=35^\circ$$. Which of the following is equal to the ratio $$\frac{AB}{AC}$$?

   • $$\frac{DE}{DF}$$
   • $$\frac{EF}{DF}$$
   • $$\frac{DF}{EF}$$
   • $$\frac{DE}{EF}$$

5. In triangles $$ABC$$ and $$DEF$$, angles $$B$$ and $$E$$ each have measure $$60^\circ$$, and angles $$C$$ and $$F$$ each have measure $$45^\circ$$. Which additional piece of information is sufficient to determine whether triangle $$ABC$$ is congruent to triangle $$DEF$$?

   • The measure of angle $$A$$
   • The length of side $$AB$$
   • The lengths of sides $$BC$$ and $$EF$$
   • No additional information is necessary.

6. Lines $$l$$ and $$m$$ are parallel. Two diagonals intersect between the lines as shown. At the intersection of the diagonals, one of the angles is $$120^\circ$$. On line $$l$$, the angles formed with the diagonals are labeled $$x^\circ$$ and $$(3x-15)^\circ$$. What is the value of $$x$$?

   • $$18.75$$
   • $$25$$
   • $$35$$
   • $$40$$

7. In the figure above, $$EB=BA$$. What is the value of x?

   • $$45^\circ$$
   • $$50^\circ$$
   • $$60^\circ$$
   • $$70^\circ$$

8. In triangle $$XYZ$$, angle $$Z$$ is a right angle. Point $$D$$ lies on $$XY$$, point $$E$$ lies on $$YZ$$, and $$DE$$ is parallel to $$XZ$$. If the length of $$XZ$$ is $$80$$ units, the length of $$DE$$ is $$20$$ units, and the area of triangle $$XYZ$$ is $$2400$$ square units, what is the length of $$YE$$, in units?

   • $$15$$
   • $$17$$
   • $$20$$
   • $$22$$

9. In the figure, points $$P$$, $$S$$, and $$Q$$ are collinear, and $$RS$$ is parallel to $$TQ$$. In triangle $$RST$$, $$RS=RT$$. The measure of angle $$PST$$ is $$103^\circ$$, and the measure of angle $$TQS$$ is $$45^\circ$$. What is the value of a?

   • $$45^\circ$$
   • $$58^\circ$$
   • $$64^\circ$$
   • $$116^\circ$$

10. In the figure above, $$ST$$ is perpendicular to $$AB$$. The length $$AT=6$$, $$SB=12$$, and $$TB=x$$. Point $$T$$ lies on $$AB$$, and $$ST$$ represents the height of triangle $$ASB$$. The area of triangle $$ASB$$ is at least $$60$$ but no more than $$84$$. If $$ST$$ is an integer, which of the following is a possible value of $$x$$?

    • $$3\sqrt{7}$$
    • $$10$$
    • $$11$$
    • $$12$$