# Worksheet: Parallel Lines and Transversals: Angle Applications

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

Q1:

Answer the questions for the given figure. Find the value of .

Find the value of .

Q2:

In the following figure, and . Find and . • A,
• B,
• C,
• D,
• E,

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 . 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
• C32
• D58
• E70

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 . Q24:

Find the value of . Q25:

Find the values of and . • A18, 26
• B22, 22
• C9, 26
• D9, 22