# Worksheet: Parallel Lines and Transversals: Angles Applications

In this worksheet, we will practice using angle relationships formed by parallel lines and transversals to solve problems involving algebraic expressions and equations.

**Q3: **

What is the value of ?

**Q4: **

Given that , find the value of . Then use that to find the value of .

- A ,
- B ,
- C ,
- D ,

**Q5: **

Answer the questions for the given figure.

Find the value of .

Find the value of .

Find the value of .

**Q6: **

The figure shows three parallel lines.

Find the value of .

Find the value of .

**Q7: **

Work out the value of in the figure.

**Q8: **

Work out the value of in the figure.

**Q9: **

Work out the value of in the figure.

**Q10: **

Work out the value of in the figure.

**Q11: **

Find .

**Q12: **

The given figure shows a pair of parallel lines and two transversals, one of which crosses at right angles.

Write an expression for in terms of .

- A
- B
- C
- D
- E

Using this expression for , find a fully simplified expression for in terms of .

- A
- B
- C
- D
- E

**Q13: **

If and , find .

**Q14: **

Given that is parallel to , find the values of and .

- A ,
- B ,
- C ,
- D ,

**Q15: **

Find the value of .

- A
- B
- C
- D

**Q16: **

Find the value of .

- A
- B
- C
- D

**Q17: **

Find the value of .

- A
- B
- C
- D

**Q18: **

Given that , determine the measure of .

**Q19: **

Answer the questions for the given figure.

Find the value of .

Find the value of .

Find the value of .

**Q20: **

Answer the questions for the given figure.

Find the value of .

Find the value of .

Find the value of .

- A78
- B12
- C58
- D70
- E32

**Q21: **

In the figure, given that , and , determine the value of .

**Q22: **

The given figure shows two lines intersecting a pair of parallel lines, one of which intersects the lines at right angles.

Find an expression for in terms of .

- A
- B
- C
- D
- E

Using what you know about the sum of angles in a quadrilateral, find an expression for in terms of .

- A
- B
- C
- D
- E

Hence, what is true of the angular measures and ?

- A
- B
- C

**Q23: **

Given that and , find the value of .

- A
- B
- C
- D

**Q24: **

Find the value of .

**Q25: **

Find the values of and .

- A9, 22
- B18, 26
- C9, 26
- D22, 22