Question

1. Give an example of two supplementary angle.2. Give an example of two congruent angles on the inside of the four-lane expressway.3. Give an example of two congruent angles on opposite sides of the four-lane expressway.4. Give an example of two congruent angles on the same side of the two-lane road.5. suppose BX = 10 ft, GY = 16 ft, and ZY = 20 ft. How far from the expressway is point W? Explain how you found your answer. (Hint: Use a proportion to find WX)

Answer 1

1. Give an example of two supplementary angle.

2. Give an example of two congruent angles on the inside of the four-lane expressway.

3. Give an example of two congruent angles on opposite sides of the four-lane expressway.

4. Give an example of two congruent angles on the same side of the two-lane road.

5. suppose BX = 10 ft, GY = 16 ft, and ZY = 20 ft. How far from the expressway is point W? Explain how you found your answer. (Hint: Use a proportion to find WX)

Part 1

Remember that, Supplementary angles sum 180 degrees

example

m consecutive interior angles

Part 2

congruent angles

example

m< B and m by corresponding angles

Part 3

congruent angles on opposite sides

m by alternate interior angles

Part 4

two congruent angles on the same side of the two-lane road.

exanple

m by corresponding angles

Part 5

we have that

m by alternate exterior angles

so

Triangle BXW is similar to Triangle GYZ

that means

BX/GY=XW/YZ=BW/GZ

so

BX/GY=XW/YZ

substitute given values

10/16=XW/20

solve for XW

XW=(10/16)*20

XW=12.5 ft