Question

Find three angles in your home or school with measures equal to \(90^{\circ}\) three with measures less than \(90^{\circ},\) and three with measures greater than \(90^{\circ} .\) Describe where you found each angle.

Short answer

Right angles: Room corner, table edge, door frame. Acute angles: Open book, triangular window, clock at 2:30. Obtuse angles: Chair backrest, open door, irregular shelf.

Step-by-step solution

Identify the Right Angles (\text{90}^{\text{circ}})

Look around the environment to find angles that measure exactly 90 degrees. Common places to find these are corners of rooms, tables, and door frames. Find three locations and describe them.

Locate Acute Angles (less than \text{90}^{\text{circ}})

Search for angles that measure less than 90 degrees. These are often found in objects like open books, triangular shapes in objects, or the hands of a clock positioned between 12 and 3 or between 3 and 6. Find three such angles and describe where each one is found.

Find Obtuse Angles (greater than \text{90}^{\text{circ}})

Identify angles that measure greater than 90 degrees. Examples include the backrests of some chairs, open doors that are not fully opened, or objects with irregular shapes. Locate three of these angles and describe where they are positioned.

Key concepts

Understanding Right Angles

A right angle is an angle that measures exactly 90 degrees. You can find them in many places around you, often forming an 'L' shape. For example, the corners of most rooms are right angles.

• Think about the corners of your desk where the legs meet the tabletop.
• The corners of doors and windows.

Right angles are significant in construction and design because they help maintain structure and stability. If an angle seems perfect and looks like a corner, then it probably is a right angle.

What are Acute Angles?

Acute angles are angles that measure less than 90 degrees. These angles are sharp and narrow. You can find them in many everyday items.

• Consider the angle formed when you open a book just a bit.
• The hands of a clock, for instance, between 12 and 3.

Acute angles are everywhere around us in various forms. They can be found in art, such as in the leaves of flowers or the edges of stars. Whenever you see a shape that forms a point and is smaller than a right angle, you are looking at an acute angle.

Exploring Obtuse Angles

Obtuse angles measure greater than 90 degrees but less than 180 degrees. They appear wide and open and are seen less frequently in everyday items, but they're still common.

• Imagine the angle of an open door that is half-open.
• The angle between the base and backrest of a reclined chair.

Obtuse angles add interesting dynamics to shapes and can often be seen in irregular structures and designs. Whenever you come across a wide opening, you are likely looking at an obtuse angle.