As shown in the figure below,  𝐴𝐶― and  𝐵𝐷― intersect at 0. Given that 180° < x° < 360° and that x = 4y, what is the value of y

1. Break Down the Problem

To find the value of $y$, we need to analyze the relationship between $x$ and $y$ given the conditions:

• $x = 4y$
• The angle $x$ satisfies $180° < x° < 360°$

2. Relevant Concepts

Given $x = 4y$, we can substitute $x$ in the inequality: $180° < 4y < 360°$

3. Analysis and Detail

1. Establish Inequalities:

   • The lower bound: $180° < 4y \implies y > \frac{180°}{4} = 45°$
   • The upper bound: $4y < 360° \implies y < \frac{360°}{4} = 90°$

2. Combine the Results: From the inequalities obtained, we have: $45° < y < 90°$

4. Verify and Summarize

The inequalities establish the range for $y$. Since the problem specifies $180° < x° < 360°$ and $x = 4y$, we derived that $y$ must be between $45°$ and $90°$.

Final Answer

The value of $y$ lies within the range $45° < y < 90°$. However, a specific numerical value can't be determined without additional information.