1 5 Word Problem Practice Angle Relationships Answer Key

15 Word Problem Practice: Angle Relationships – Answer Key & Solutions

Are you struggling with geometry word problems involving angle relationships? Do you need a comprehensive guide to help you master this crucial topic? This detailed article provides 15 challenging word problems focusing on angle relationships, along with complete, step-by-step solutions and explanations. We'll cover various angle relationships, including complementary, supplementary, vertical, linear pairs, and angles formed by parallel lines intersected by a transversal. By the end, you'll have a firm grasp of these concepts and be able to confidently tackle any angle relationship problem.

Understanding Angle Relationships

Before we dive into the word problems, let's refresh our understanding of key angle relationships:

1. Complementary Angles:

• Definition: Two angles are complementary if their sum is 90 degrees.
• Example: If angle A and angle B are complementary, and angle A = 30°, then angle B = 60° (90° - 30° = 60°).

2. Supplementary Angles:

• Definition: Two angles are supplementary if their sum is 180 degrees.
• Example: If angle X and angle Y are supplementary, and angle X = 110°, then angle Y = 70° (180° - 110° = 70°).

3. Vertical Angles:

• Definition: Vertical angles are the angles opposite each other when two lines intersect. They are always equal.
• Example: If angle P and angle Q are vertical angles, and angle P = 45°, then angle Q = 45°.

4. Linear Pairs:

• Definition: A linear pair consists of two adjacent angles that form a straight line. Their sum is always 180 degrees.
• Example: If angle A and angle B are a linear pair, and angle A = 120°, then angle B = 60° (180° - 120° = 60°).

5. Angles Formed by Parallel Lines and a Transversal:

• Definition: When a transversal intersects two parallel lines, several angle relationships are formed:
  • Corresponding Angles: These angles are in the same relative position at each intersection and are equal.
  • Alternate Interior Angles: These angles are between the parallel lines and on opposite sides of the transversal; they are equal.
  • Alternate Exterior Angles: These angles are outside the parallel lines and on opposite sides of the transversal; they are equal.
  • Consecutive Interior Angles (Same-Side Interior Angles): These angles are between the parallel lines and on the same side of the transversal; they are supplementary.

15 Word Problems on Angle Relationships

Now, let's tackle the word problems. Remember to draw diagrams to visualize the problem!

Problem 1: Two angles are complementary. One angle is 25 degrees more than the other. Find the measure of each angle.

Problem 2: Two angles are supplementary. One angle is three times the measure of the other. Find the measure of each angle.

Problem 3: Two angles are vertical angles. One angle measures 72 degrees. What is the measure of the other angle?

Problem 4: Angles A and B are a linear pair. Angle A measures 115 degrees. What is the measure of angle B?

Problem 5: Lines l and m are parallel. A transversal intersects them. If one of the alternate interior angles is 60 degrees, what is the measure of its corresponding angle?

Problem 6: Two angles are complementary. One angle is twice the measure of the other. Find the measure of each angle.

Problem 7: Two angles are supplementary. One angle is 40 degrees less than the other. Find the measure of each angle.

Problem 8: Find the measure of the vertical angle to an angle measuring 135 degrees.

Problem 9: Angles P and Q are a linear pair. Angle P is 20 degrees larger than angle Q. Find the measure of each angle.

Problem 10: Lines x and y are parallel. A transversal intersects them. If one of the consecutive interior angles is 105 degrees, what is the measure of the other consecutive interior angle?

Problem 11: Two angles are complementary. Their difference is 20 degrees. Find the measure of each angle.

Problem 12: Two angles are supplementary. One angle is 5 times the measure of the other. Find the measure of each angle.

Problem 13: A transversal intersects two parallel lines. If one of the alternate exterior angles is 85 degrees, what is the measure of its corresponding alternate exterior angle?

Problem 14: Angles R and S are a linear pair. The measure of angle R is twice the measure of angle S. Find the measure of each angle.

Problem 15: Lines a and b are parallel. A transversal intersects them. One of the alternate interior angles is 4x + 10 degrees, and the other is 6x - 20 degrees. Find the value of x and the measure of each angle.

Answer Key and Detailed Solutions

Here are the solutions to the 15 word problems, explained step-by-step:

Problem 1: Let the angles be x and x + 25. Since they are complementary, x + (x + 25) = 90. Solving for x, we get 2x = 65, so x = 32.5. The angles are 32.5 degrees and 57.5 degrees.

Problem 2: Let the angles be x and 3x. Since they are supplementary, x + 3x = 180. Solving for x, we get 4x = 180, so x = 45. The angles are 45 degrees and 135 degrees.

Problem 3: Vertical angles are equal, so the other angle also measures 72 degrees.

Problem 4: Linear pairs are supplementary, so angle B = 180 - 115 = 65 degrees.

Problem 5: Corresponding angles are equal, so the corresponding angle also measures 60 degrees.

Problem 6: Let the angles be x and 2x. Since they are complementary, x + 2x = 90. Solving for x, we get 3x = 90, so x = 30. The angles are 30 degrees and 60 degrees.

Problem 7: Let the angles be x and x - 40. Since they are supplementary, x + (x - 40) = 180. Solving for x, we get 2x = 220, so x = 110. The angles are 110 degrees and 70 degrees.

Problem 8: The vertical angle also measures 135 degrees.

Problem 9: Let the angles be x and x + 20. Since they are a linear pair, x + (x + 20) = 180. Solving for x, we get 2x = 160, so x = 80. The angles are 80 degrees and 100 degrees.

Problem 10: Consecutive interior angles are supplementary, so the other consecutive interior angle is 180 - 105 = 75 degrees.

Problem 11: Let the angles be x and x + 20. Since they are complementary, x + (x + 20) = 90. Solving for x, we get 2x = 70, so x = 35. The angles are 35 degrees and 55 degrees.

Problem 12: Let the angles be x and 5x. Since they are supplementary, x + 5x = 180. Solving for x, we get 6x = 180, so x = 30. The angles are 30 degrees and 150 degrees.

Problem 13: Alternate exterior angles are equal, so the other alternate exterior angle also measures 85 degrees.

Problem 14: Let the angles be x and 2x. Since they are a linear pair, x + 2x = 180. Solving for x, we get 3x = 180, so x = 60. The angles are 60 degrees and 120 degrees.

Problem 15: Alternate interior angles are equal, so 4x + 10 = 6x - 20. Solving for x, we get 2x = 30, so x = 15. The angles are 4(15) + 10 = 70 degrees and 6(15) - 20 = 70 degrees.

This comprehensive guide provides a solid foundation for understanding and solving word problems involving angle relationships. Remember to practice regularly and visualize the problems using diagrams for better comprehension. Consistent practice will boost your confidence and mastery of this important geometry topic. Good luck!