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Chapter 9: Problem 5

Classify each angle as acute, obtuse, right, or straight. $$55^{\circ}$$

Short Answer

Expert verified
The angle is acute.

Step by step solution

01

Understanding Angle Types

Angles are classified based on their measures: acute (less than 90掳), right (exactly 90掳), obtuse (more than 90掳 but less than 180掳), and straight (exactly 180掳).
02

Comparing with the Definition of Acute Angles

First, we need to determine if the angle measure falls into the category of an acute angle. Since an acute angle is less than 90掳, check if 55掳 is less than 90掳.
03

Conclusion from Comparison

Since 55掳 is less than 90掳, it fits the definition of an acute angle. Therefore, 55掳 qualifies as an acute angle.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Acute Angles
Acute angles are those which are smaller than a right angle. Specifically, any angle that measures less than 90 degrees is considered acute. This means that if you have an angle measuring 55 degrees, like the one in the exercise, it would be classified as an acute angle.

  • Acute angles are always less than 90掳.
  • Their measurements are typically noted as a smaller slant or incline in visual representations of angles.
  • They are commonly seen in various geometric shapes such as triangles, particularly in equilateral and acute triangles where all angles are acute.

Understanding acute angles is essential in geometry as they often appear when analyzing different shapes or solving for unknown angles.
Obtuse Angles
An obtuse angle is one that measures more than a right angle but less than a straight angle. This means it measures between 90掳 and 180掳. For instance, if you have an angle measuring 120掳, it is considered obtuse. These angles appear less frequently than acute angles in simple geometric figures, but they are crucial for understanding more complex shapes and problems.

  • Obtuse angles range from 90掳 to 179掳.
  • They often form larger, more open arcs in diagrams.
  • Commonly found in obtuse triangles, where one angle specifically measures more than 90掳.

Studying obtuse angles helps in understanding the relationships between different lengths and angles in plane figures.
Types of Angles
Angles can be categorized depending on their degree measures. In geometry, understanding the different types of angles is fundamental as it allows us to classify and solve various problems involving angles. The main types of angles you will encounter are:
  • Acute Angles: Less than 90掳.
  • Right Angles: Exactly 90掳.
  • Obtuse Angles: Between 90掳 and 180掳.
  • Straight Angles: Exactly 180掳, appearing as straight lines.

Understanding these classifications help you to properly analyze shapes and execute accurate calculations. For instance, knowing an angle is acute aids in trigonometric calculations where precise angle measure is critical. Angle classification is not just about knowing their measures but also interpreting their role in geometry.

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