Lines & Angles & Triangles 2 — Geometry and Trigonometry

Questions in this quiz (6)

1. Triangles $$DEF$$ and $$UVW$$ are graphed in the $$xy$$-plane. Triangle $$DEF$$ has vertices $$D(1,4)$$, $$E(4,10)$$, and $$F(7,4)$$. Triangle $$UVW$$ has vertices $$U(2,3)$$, $$V(2+2k,3+4k)$$, and $$W(2+6k,3)$$, where $$k$$ is a positive constant. If the measure of $$\angle F$$ is $$t^\circ$$, what is the measure of $$\angle W$$?

   • $$(90-t)^\circ$$
   • $$t^\circ$$
   • $$(t+30)^\circ$$
   • $$(180-t)^\circ$$

2. In the figure shown, points $$D,F,C,$$ and $$E$$ lie on line segment $$AB$$, and line segment $$FH$$ intersects line segment $$CG$$ at point $$I$$. The measure of $$\angle CDG$$ is $$50^\circ$$, the measure of $$\angle CGD$$ is $$65^\circ$$, the measure of $$\angle CIH$$ is $$122^\circ$$, and the measure of $$\angle BEH$$ is $$114^\circ$$. What is the measure, in degrees, of $$\angle EHF$$?

   • 9°
   • 57°
   • 60°
   • 65°

3. Triangle $$DEF$$ is an isosceles triangle with base angles measuring $$57^\circ$$. Triangle $$D'E'F'$$ is similar to triangle $$DEF$$. The length of each side of triangle $$D'E'F'$$ is one-third as large as the corresponding side of triangle $$DEF$$. What is the measure of each of the base angles of triangle $$D'E'F'$$?

   • $$19^\circ$$
   • $$57^\circ$$
   • $$90^\circ$$
   • $$171^\circ$$

4. In the figure above, $$AB=BE$$. The measure of angle $$DCB$$ is $$30^\circ$$, and the measure of angle $$ABE$$ is $$104^\circ$$. What is the value of x?

   • $$112$$
   • $$76$$
   • $$68$$
   • $$38$$

5. Intersecting lines $$A$$, $$B$$, and $$C$$ are shown above. What is the value of $$x$$?

   • $$84$$
   • $$96$$
   • $$97$$
   • $$98$$

6. Triangle $$GHI$$ is an isosceles triangle with base angles measuring $$64^\circ$$. Triangle $$G'H'I'$$ is similar to triangle $$GHI$$. The length of each side of triangle $$G'H'I'$$ is one-half the length of the corresponding side of triangle $$GHI$$. What is the measure of each base angle of triangle $$G'H'I'$$?

   • $$32^\circ$$
   • $$64^\circ$$
   • $$90^\circ$$
   • $$128^\circ$$