Geometry and Trigonometry - Lines, angles, and triangles — Quiz 3

Questions in this quiz (10)

1. For the triangles shown, triangle $$ABC$$ is dilated by a scale factor of $$3$$ to obtain triangle $$XYZ$$, where $$d=16$$. What is the measure, in degrees, of angle $$X$$?

   • $$20$$
   • $$57$$
   • $$60$$
   • $$63$$

2. In the given figure, $$\overline{AC}$$ extends to point $$D$$. If the measure of $$\angle BAC$$ is equal to the measure of $$\angle BCA$$, what is the value of $$x$$?

   • $$110$$
   • $$70$$
   • $$55$$
   • $$40$$

3. In the figure shown, triangle $$CAE$$ is similar to triangle $$CBD$$. The measure of angle $$CBD$$ is $$57^\circ$$, and $$AE=26(BD)$$. What is the measure of angle $$CAE$$?

   • $$(26\cdot57)^\circ$$
   • $$(26+57)^\circ$$
   • $$57^\circ$$
   • $$26^\circ$$

4. In triangle $$ABC$$, angle $$B$$ is a right angle. Point $$D$$ lies on $$AC$$, and point $$E$$ lies on $$AB$$ such that $$DE$$ is parallel to $$BC$$. If the measure of angle $$ABC$$ is $$90^\circ$$ and the measure of angle $$ACB$$ is $$28^\circ$$, what is the measure, in degrees, of angle $$AED$$?

   • 90

5. Quadrilaterals $$LMNO$$ and $$PQRS$$ are similar, where $$L$$, $$M$$, and $$N$$ correspond to $$P$$, $$Q$$, and $$R$$, respectively. The measure of $$\angle O$$ is $$120^\circ$$. What is the measure of $$\angle S$$?

   • $$30^\circ$$
   • $$60^\circ$$
   • $$120^\circ$$
   • $$240^\circ$$

6. In triangle $$XYZ$$, the measure of angle $$X$$ is $$40^\circ$$. If triangle $$XYZ$$ is isosceles, which of the following is NOT a possible measure of angle $$Y$$?

   • $$40^\circ$$
   • $$50^\circ$$
   • $$70^\circ$$
   • $$100^\circ$$

7. In right triangle $$DEF$$, angle $$F$$ is the right angle and $$EF=120$$. Point $$G$$ lies on side $$DF$$, and point $$H$$ lies on side $$DE$$ such that $$GH$$ is parallel to $$EF$$ and $$DG=3GF$$. What is the length of line segment $$GH$$?

   • 90

8. Triangle $$PQR$$ is similar to triangle $$XYZ$$, where $$P$$, $$Q$$, and $$R$$ correspond to $$X$$, $$Y$$, and $$Z$$, respectively. In triangle $$PQR$$, the length of $$PQ$$ is $$90$$ and the length of $$QR$$ is $$180$$. In triangle $$XYZ$$, the length of $$YZ$$ is $$30$$. What is the length of $$XY$$?

   • $$15$$
   • $$30$$
   • $$45$$
   • $$60$$

9. A line intersects two parallel lines, forming acute and obtuse angles. The measure of one acute angle is $$(5x+20)^\circ$$, and the adjacent obtuse angle is $$(12x-10)^\circ$$. What is the value of $$x$$?

   • 10

10. In triangle $$DEF$$, the measure of angle $$D$$ is $$62^\circ$$, the measure of angle $$E$$ is $$90^\circ$$, and the measure of angle $$F$$ is $$\left(\frac{m}{2}\right)^\circ$$. What is the value of $$m$$?

    • $$56$$
    • $$72$$
    • $$76$$
    • $$112$$