Introduction

Angle relationships are a fundamental concept in geometry, and they play a crucial role in solving various problems. In this article, we will discuss the Angle Relationships Homework 2 Answer Key, which will help you understand the essential concepts of angle relationships and solve the given problems with ease.

What are Angle Relationships?

Angle relationships refer to the various ways in which angles can be related to one another. These relationships include complementary angles, supplementary angles, adjacent angles, vertical angles, and alternate interior angles.

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. For example, if angle A measures 30 degrees, then the complementary angle B will measure 60 degrees.

Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. For example, if angle C measures 120 degrees, then the supplementary angle D will measure 60 degrees.

Adjacent Angles

Adjacent angles are two angles that share a common vertex and a common side. For example, if angle E and angle F share a common vertex and a common side, they are said to be adjacent angles.

Vertical Angles

Vertical angles are two angles that share a common vertex but do not share a common side. For example, if angle G and angle H share a common vertex but do not share a common side, they are said to be vertical angles.

Alternate Interior Angles

Alternate interior angles are two angles that are on opposite sides of a transversal and inside the two lines. For example, if angle I and angle J are on opposite sides of a transversal and inside the two lines, they are said to be alternate interior angles.

Angle Relationships Homework 2 Answer Key

Now that we have discussed the various angle relationships, let us look at the Angle Relationships Homework 2 Answer Key. The given problem set contains various questions related to angle relationships, and the answer key will help you solve them with ease.

Problem 1

If angle A and angle B are complementary angles, and angle A measures 30 degrees, what is the measure of angle B?

Solution: As angle A and angle B are complementary angles, their measures add up to 90 degrees. Therefore, angle B must measure 60 degrees.

Problem 2

If angle C and angle D are supplementary angles, and angle C measures 120 degrees, what is the measure of angle D?

Solution: As angle C and angle D are supplementary angles, their measures add up to 180 degrees. Therefore, angle D must measure 60 degrees.

Problem 3

If angle E and angle F are adjacent angles, and angle E measures 60 degrees, what is the measure of angle F?

Solution: As angle E and angle F are adjacent angles, they share a common vertex and a common side. Therefore, angle F must measure 120 degrees.

Problem 4

If angle G and angle H are vertical angles, and angle G measures 100 degrees, what is the measure of angle H?

Solution: As angle G and angle H are vertical angles, they share a common vertex but do not share a common side. Therefore, angle H must also measure 100 degrees.

Problem 5

If angle I and angle J are alternate interior angles, and angle I measures 70 degrees, what is the measure of angle J?

Solution: As angle I and angle J are alternate interior angles, they are on opposite sides of a transversal and inside the two lines. Therefore, angle J must also measure 70 degrees.

Conclusion

Angle relationships are an important concept in geometry, and understanding them is crucial for solving various problems. By using the Angle Relationships Homework 2 Answer Key, you can easily solve the given problems and strengthen your understanding of angle relationships.