# Worksheet: Angle Relationships

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

**Q4: **

Determine and in the given figure.

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

**Q6: **

Determine .

**Q7: **

If and , find .

**Q8: **

If the measure of an angleβs supplement is 6 more than three 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 .