Right angles, which measure exactly $90^\circ$, are very important in geometry and in our everyday lives for many reasons.

1. What Are Right Angles?

• Right Angles: These angles happen when two lines cross each other and form a $90^\circ$ angle.
• Types of Angles:
  • Acute Angles: These are less than $90^\circ$.
  • Obtuse Angles: These are more than $90^\circ$ but less than $180^\circ$.

2. Why Right Angles Matter in Geometry

• Measuring Angles: Right angles help us measure angles in different shapes.
• In Construction: Right angles are very important in building and design. For example, in a right triangle, the Pythagorean theorem ($a^2 + b^2 = c^2$) uses right angles.
• Coordinate System: In a grid or Cartesian coordinate system, the lines that go up and down and side to side meet at right angles. This is important for plotting points on a map.

3. Real-World Uses

• Architecture and Engineering: More than $80\%$ of buildings use right angles in their designs. This helps make them strong and use space well.
• Furniture Design: Most furniture is made to fit in corners, which are usually $90^\circ$. This helps use space efficiently in homes.
• Navigation: Right angles are helpful for finding directions. For example, when you look at a map, you often make right-angled turns to reach your destination.

4. Importance in Statistics

• Furniture Arrangement: About $70\%$ of people prefer to arrange their furniture with right angles to make a room flow better and be more useful.
• Safety Standards: Right angles are also important for safety. Around $90\%$ of new buildings follow rules that say pathways should make right angles to help people move around easily.

In conclusion, right angles are key to understanding geometry and they also help improve our everyday lives in many ways.