Geometry and Trigonometry - Lines, angles, and triangles — Quiz 4

Questions in this quiz (10)

1. In the figure shown, $$\overline{WZ}$$ and $$\overline{XY}$$ intersect at point $$Q$$. $$YQ=63$$, $$WQ=70$$, $$WX=60$$, and $$XQ=120$$. What is the length of $$\overline{YZ}$$?

   • 54

2. In the figure, $$RT=TU$$, the measure of angle $$VST$$ is $$29^\circ$$, and the measure of angle $$RVS$$ is $$41^\circ$$. What is the value of $$x$$?

   • 156

3. In triangle $$MNP$$, the measures of $$\angle N$$ and $$\angle P$$ are each $$52^\circ$$. What is the measure of $$\angle M$$, in degrees?

   • 76

4. In triangle $$GHI$$, the measure of angle $$G$$ is $$58^\circ$$ and the measure of angle $$H$$ is $$102^\circ$$. In triangle $$JKL$$, the measure of angle $$J$$ is $$58^\circ$$ and the measure of angle $$K$$ is $$102^\circ$$. Which of the following additional pieces of information is needed to determine whether triangle $$GHI$$ is similar to triangle $$JKL$$?

   • $$The\ measure\ of\ angle\ I$$
   • $$The\ measure\ of\ angle\ L$$
   • $$The\ measure\ of\ angle\ I\ and\ the\ measure\ of\ angle\ L$$
   • $$No\ additional\ information\ is\ needed$$

5. Each side of equilateral triangle $$A$$ is multiplied by a scale factor of $$k$$ to create equilateral triangle $$B$$. The length of each side of triangle $$B$$ is greater than the length of each side of triangle $$A$$. Which of the following could be the value of $$k$$?

   • $$\frac{31}{30}$$
   • $$1$$
   • $$\frac{30}{31}$$
   • $$0$$

6. In convex pentagon $$PQRST$$, segment $$PQ$$ is parallel to segment $$ST$$. The measure of angle $$Q$$ is $$128^\circ$$, and the measure of angle $$S$$ is $$168^\circ$$. What is the measure, in degrees, of angle $$R$$?

   • 64

7. Triangles $$UVW$$ and $$XYZ$$ are congruent, where $$U$$ corresponds to $$X$$, and $$V$$ and $$Y$$ are right angles. The measure of angle $$U$$ is $$64^\circ$$. What is the measure, in degrees, of angle $$Z$$?

   • 26

8. Triangles $$ABC$$ and $$DEF$$ are graphed in the $$xy$$-plane. Triangle $$ABC$$ has vertices $$A(2,4)$$, $$B(2,8)$$, and $$C(6,4)$$. Triangle $$DEF$$ has vertices $$D(2,4)$$, $$E(2,8+m)$$, and $$F(6+m,4)$$, where $$m$$ is a positive constant. If the measure of $$\angle B$$ is $$t^\circ$$, what is the measure of $$\angle E$$?

   • $$t^\circ$$
   • $$(t+m)^\circ$$
   • $$(t-m)^\circ$$
   • $$(90-t)^\circ$$

9. 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 $$48^\circ$$, the measure of $$\angle SXQ$$ is $$86^\circ$$, the measure of $$\angle SWU$$ is $$85^\circ$$, and the measure of $$\angle VTU$$ is $$162^\circ$$. What is the measure, in degrees, of $$\angle TUR$$?

   • 49

10. In the figure above, $$RT=TU$$. What is the value of $$x$$?

    • $$72$$
    • $$66$$
    • $$64$$
    • $$58$$