# Worksheet: Using Angle Relationships to Solve Algebraic Expressions

Q1:

Answer the following questions using the given diagram.

Form an equation that will allow you to calculate .

• A
• B
• C
• D
• E

Find the value of .

• A
• B
• C
• D
• E

Q2:

If is an altitude of , , and , find .

Q3:

Find the values of and so that and are perpendicular.

• A ,
• B ,
• C ,
• D ,
• E ,

Q4:

In the given diagram, is a straight line, , and .

Form an equation that will allow you to calculate .

• A
• B
• C
• D
• E

Solve for .

• A
• B
• C
• D
• E

Q5:

Answer the following questions using the given diagram.

Form an equation that will allow you to calculate .

• A
• B
• C
• D
• E

Find the value of .

• A
• B
• C
• D
• E

Q6:

In the given diagram, is a right angle and is twice . Let .

Form an equation that will allow you to calculate .

• A
• B
• C
• D
• E

Solve for .

• A
• B
• C
• D
• E

Q7:

In the given diagram, and are straight lines. Answer the following questions.

Form an equation that will allow you to calculate .

• A
• B
• C
• D
• E

Find the value of .

• A
• B
• C
• D
• E

Find the value of .

• A
• B
• C
• D
• E

Find the value of .

• A
• B
• C
• D
• E

Q8:

Quadrilateral is a rectangle. If and , find .

Q9:

In the given diagram, is a straight line. Answer the following questions.

Form an equation that will allow you to calculate .

• A
• B
• C
• D
• E

Find the value of .

• A
• B
• C
• D
• E

Q10:

In this figure, and form a linear pair. If , , and , determine .

Q11:

Answer the following questions using the given diagram.

Form an equation that will allow you to calculate .

• A
• B
• C
• D
• E

Find the value of .

• A
• B
• C
• D
• E

Q12:

The given figure shows two intersecting lines.

Find an expression for in terms of .

• A
• B
• C
• D
• E

Find an expression for in terms of .

• A
• B
• C
• D
• E

Hence, what is true of and ?

• AThey are supplementary.
• BThey are complementary.
• CThey are equal.

We have worked out that . Use this to find an expression for in terms of .

• A
• B
• C
• D
• E

Q13:

In the given diagram, and . Find the value of .

• A
• B
• C
• D
• E

Q14:

Find .

• A
• B
• C
• D

Q15:

In the given diagram, and are straight lines. Answer the following questions.

Form an equation that will allow you to calculate .

• A
• B
• C
• D
• E

Find the value of .

• A
• B
• C
• D
• E

Find the value of .

• A
• B
• C
• D
• E

Find the value of .

• A
• B
• C
• D
• E

Q16:

In the given figure, and are opposite rays, and bisects . If and , find .

Q17:

If , , and , find the measure of each angle.

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q18:

In the given figure, find the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q19:

From the intersecting lines in the figure, determine the value of .

Q20:

In the figure below, and are opposite rays, and bisects . If and , find .