# Lesson Worksheet: Angle Relationships Mathematics • 7th Grade

In this worksheet, we will practice solving problems involving algebraic expressions and equations using the relationships between complementary, supplementary, adjacent, and vertically opposite angles.

Q1:

What is the measure of ? Q2:

Find . Q3:

Find , , and . • A, ,
• B, ,
• C, ,
• D, ,

Q4:

Determine and in the given figure. • A,
• B,
• C,
• D,
• E,

Q5:

Find . Q6:

Determine . Q7:

If and , find . Q8:

If the measure of an angle’s supplement is 6 more than 3 times the measure of its complement, what is the measure of that angle?

Q9:

Given the following figure, find . Q10:

and are two intersecting straight lines. Given that and , find . Q11:

If and form a linear pair, where and , determine and . • A,
• B,
• C,
• D,
• E,

Q12:

These two angles are supplementary. Write and solve an equation to find .

Recall that two angles are supplementary if the sum of their measures is . • A,
• B,
• C,
• D,
• E,

Q13:

The rays and are perpendicular. A point lies in the interior of . Given that and , find and .

• A,
• B,
• C,
• D,
• E,

Q14:

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

Q15:

Given that and , find . Q16:

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

Q17:

Using the fact that the lines in the figure intersect, find the values of and . • A,
• B,
• C,
• D,
• E,

Q18:

If and are supplementary, and the measure of is more than the measure of , find the measure of each angle.

• A,
• B,
• C,
• D,
• E,

Q19:

If is an altitude of , , and , find . Q20:

Find the values of and so that and are perpendicular. • A,
• B,
• C,
• D,
• E,

Q21:

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

Q22:

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

Q23:

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

Q24:

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

Q25:

Quadrilateral is a rectangle. If and , find . 