Worksheet: Applications of Parallel Lines

Q1:

In the given figure, find the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q2:

In the given figure, find the values of and .

• A ,
• B ,
• C ,
• D ,

Q3:

Find the values of and .

• A ,
• B ,
• C ,
• D ,

Q4:

Find the values of and .

• A ,
• B ,
• C ,
• D ,

Q5:

If , what is ?

Q6:

In the diagram below, , , , , and . Find the value of and the length of .

• A ,
• B ,
• C ,
• D ,

Q7:

In the figure, , , , and . Find the value of .

Q8:

In the figure, , , , and . Find the value of .

Q9:

Using the information in the figure, determine the length of .

Q10:

Given that , , , and , find the length of and .

• A ,
• B ,
• C ,
• D ,

Q11:

Given the following figure, find the numerical values of and .

• A ,
• B ,
• C ,
• D ,

Q12:

Given the following figure, find the numerical values of and .

• A ,
• B ,
• C ,
• D ,

Q13:

In the figure, given that , what is ?

Q14:

Find the lengths of and .

• A ,
• B ,
• C ,
• D ,

Q15:

Given that cm, cm, cm, , , and , find the values of and .

• A ,
• B ,
• C ,
• D ,

Q16:

Given that cm, cm, cm, , and , find the lengths of and .

• A ,
• B ,
• C ,
• D ,

Q17:

In the following figure, , , , and . Find the values of and .

• A ,
• B ,
• C ,
• D ,

Q18:

In the following figure, , , , and . Find the values of and .

• A ,
• B ,
• C ,
• D ,

Q19:

In the figure, lines , and are all parallel. Given that , , , and , what is the length of ?

Q20:

Given that , , and , determine the values of and .

• A ,
• B ,
• C ,
• D ,

Q21:

Given that , , and , determine the values of and .

• A ,
• B ,
• C ,
• D ,

Q22:

Given that , , , and , determine the lengths of and .

• A 36 cm, 22.5 cm
• B 37.5 cm, 42 cm
• C 67.2 cm, 22.5 cm
• D 36 cm, 42 cm

Q23:

Given that , , , and , determine the lengths of and .

• A 50.4 cm, 31.5 cm
• B 52.5 cm, 55.5 cm
• C 88.8 cm, 31.5 cm
• D 50.4 cm, 55.5 cm

Q24:

Given that , , , and , find the value of .

Q25:

Given that , , , and , find the value of .