1-5 word problem practice angle relationships answer key

Lemon

2 min read

·

02-02-2025

1

0

Share

This answer key provides solutions for 1-5 word problems focusing on angle relationships. Remember to always show your work, as the process is as important as the final answer. Understanding the why behind the solution is key to mastering angle relationships.

Before we begin, let's review some key angle relationship definitions:

• Complementary Angles: Two angles whose measures add up to 90 degrees.
• Supplementary Angles: Two angles whose measures add up to 180 degrees.
• Vertical Angles: Angles opposite each other when two lines intersect. They are always congruent (equal).
• Linear Pair: Two adjacent angles that form a straight line (their measures add up to 180 degrees).

Now, let's tackle some example problems (replace these with your actual problems):

Problem 1: Two angles are complementary. One angle measures 35 degrees. What is the measure of the other angle?

Answer 1: Complementary angles add up to 90 degrees. Therefore, the other angle measures 90 - 35 = 55 degrees.

Problem 2: Angles A and B are supplementary. Angle A measures 110 degrees. Find the measure of angle B.

Answer 2: Supplementary angles add up to 180 degrees. So, angle B measures 180 - 110 = 70 degrees.

Problem 3: Two lines intersect, forming four angles. One angle measures 60 degrees. What are the measures of the other three angles?

Answer 3: Vertical angles are equal. Therefore, the angle directly opposite the 60-degree angle also measures 60 degrees. The other two angles form a linear pair with the 60-degree angle. Since a linear pair adds up to 180 degrees, the other two angles each measure 180 - 60 = 120 degrees.

Problem 4: Angle X and Angle Y are vertical angles. Angle X is twice the measure of Angle Y. Find the measure of both angles.

Answer 4: Let's say Angle Y = x. Then Angle X = 2x. Since they are vertical angles, they are equal: x = 2x. This means x must equal 0, which isn't possible for angles in geometry. There must be a mistake in the problem's wording. Vertical angles are equal, not that one is twice the other. If the problem meant they are supplementary or complementary, we could solve it. Let’s assume it is a supplementary relationship and solve accordingly: x + 2x = 180. Solving this, 3x = 180 and x = 60. Therefore, Angle Y = 60 degrees and Angle X = 120 degrees.

Problem 5: A triangle has angles measuring x, 2x, and 3x. Find the value of x and the measure of each angle.

Answer 5: The sum of angles in a triangle is always 180 degrees. Therefore: x + 2x + 3x = 180. This simplifies to 6x = 180, so x = 30. The angles measure 30 degrees, 60 degrees, and 90 degrees.

Remember: These are examples. Substitute your actual problems into this framework. Clearly define the angle relationship, set up your equation, and solve for the unknown. Always double-check your work and consider the context of the problem to ensure your solution makes sense within the geometric context.