https://file.aiquickdraw.com/mathbot/file/1729172387412fbnn5xun.jpg

For this truss to pass inspection, the top and bottom portions must be parallel. What values should ∠x and ∠y be?

To determine the values of angles \( x^\circ \) and \( y^\circ \), we can use properties of parallel lines and angles in a triangle.

### Step-by-step Solution:

#### 1. Using the fact that the top and bottom lines are parallel:

- The two angles of \( 55^\circ \) are alternate interior angles, because the top and bottom lines are parallel, and the lines creating the angles act like transversals.
- This means that the triangles on either side of the middle triangle are isosceles, and each base angle is \( 55^\circ \).

#### 2. Find \( x^\circ \):

- In the middle triangle, we know one angle is \( 55^\circ \). Since the angles in a triangle sum to \( 180^\circ \), we can find \( x \) by subtracting the known angles:
  \[
  x^\circ = 180^\circ - 55^\circ - 55^\circ = 70^\circ
  \]

#### 3. Find \( y^\circ \):

- On the right side of the diagram, we have a triangle where one angle is \( 55^\circ \) and the interior angle \( y^\circ \) is adjacent to it. Since these two angles form a straight line (sum to \( 180^\circ \)), we can find \( y \) as:
  \[
  y^\circ = 180^\circ - 55^\circ = 125^\circ
  \]

### Final Answers:
- \( x = 70^\circ \)
- \( y = 125^\circ \)

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What is the sum of interior angles in any triangle?
2. How do alternate interior angles help determine parallel lines?
3. How do you calculate the third angle in a triangle if two angles are known?
4. What is the relationship between adjacent angles on a straight line?
5. How do isosceles triangles help solve for missing angles?

**Tip:** Remember that when two lines are parallel, alternate interior angles are always congruent.

For this truss to pass inspection, the top and bottom portions must be parallel. What values should ∠x and ∠y be?

Learn how to solve for angles x and y in a truss where the top and bottom lines are parallel. This geometry problem involves the use of alternate interior angles and the angle sum theorem in triangles. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation