Question

Mara is building a set of shelves supported by a diagonal brace, as shown in the diagram. Answer the questions to decide whether all three shelves are parallel. 1. If ∠2 measures 120°, what is the measure of ∠1? Explain how you found the measure of ∠1. (The image) Write your answer in the space below. 2. Think of the top and middle shelves as two lines cut by a transversal. What type of angles are ∠1 and ∠5? Write your answer in the space below. 3. Use the relationship between ∠1 and ∠5 to decide whether the top and middle shelves are parallel. Write your answer in the space below. 4. Is the bottom shelf parallel to the top shelf? Explain. Write your answer in the space below. 5. Is the bottom shelf parallel to the middle shelf? Explain. Write your answer in the space below.

Answer 1

Answer:

Step-by-step explanation:

1). Since, m∠1 + m∠2 = 180° [Supplementary angles]

   If m∠2 = 120°

   m∠1 + 120° = 180°

   m∠1 = 180° - 120°

   m∠1 = 60°

2). If a transversal intersects two parallel lines on the top and middle,

   ∠1 and ∠5 will be corresponding angles.

3). Since, m∠1 = m∠5 = 60° (Corresponding angles)

   Therefore, both the lines on top and middle will be parallel.

4). Since, m∠9 + m∠11 = 180° [Supplementary angles]

   If m∠11 = 120°

   m∠9 + 120° = 180°

   m∠9 = 60°

   Since, m∠1 = m∠9 = 60° [Corresponding angles]

   Therefore, both the lines on the top and bottom shelves will be parallel.

5). Since, m∠5 = m∠9 = 60° [Corresponding angles]

    Therefore, middle and bottom shelves will be parallel.