Math Problem Statement

ANSWER

The diagram shows three squares of the same size. What is the value of x?

Solution

To solve this problem, let's analyze the diagram carefully. The three squares are arranged in such a way that the angles where they meet form right angles. Since the squares are all of the same size, each internal angle of a square is 90°.

From the image, we can see that the angle labeled as "x" is formed between two squares meeting at the center. We can assume that the total angle around the point where the squares meet is 360°.

The three squares meet at three corners, creating three angles of 90° each. So, the remaining angle (x) must satisfy:

x+90°+90°+90°=360°x + 90° + 90° + 90° = 360°

Simplifying this:

x+270°=360°x + 270° = 360°

x=360°270°x = 360° - 270°

x=90°x = 90°

Thus, the value of xx is 90°.

If you have any questions or need further clarification, feel free to ask!

Here are some related questions:

  1. How would the angle change if there were only two squares instead of three?
  2. Can you explain why the sum of the angles at a point is always 360°?
  3. What would happen if the squares had different sizes?
  4. How can we prove the sum of the angles inside a square is always 360°?
  5. What other geometric shapes could form a similar configuration?

Tip: Always remember that the total angle around any point in geometry is 360°, and use this property to solve problems involving angles formed by shapes.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles
Squares

Formulas

Sum of angles around a point is 360°

Theorems

Angle sum around a point theorem

Suitable Grade Level

Grades 6-8