Obtuse Angle

Definition

An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. This type of angle plays a key role in understanding various properties and relationships within geometric figures, particularly triangles, where the presence of an obtuse angle affects the classification and measurement of the triangle's angles. Recognizing obtuse angles also helps when working with points, lines, and planes, as they can influence how angles are measured and compared.

5 Must Know Facts For Your Next Test

1. In any triangle, if one angle is obtuse, the other two angles must be acute, as their measures must add up to 180 degrees.
2. An obtuse triangle is defined as a triangle that has one obtuse angle and two acute angles.
3. The sum of the interior angles of a triangle, including those with an obtuse angle, will always equal 180 degrees.
4. Obtuse angles can be found in various geometric figures, not just triangles, such as quadrilaterals where an obtuse angle may contribute to the overall shape.
5. When measuring angles using a protractor, any measurement greater than 90 degrees but less than 180 degrees indicates an obtuse angle.

Review Questions

• How does the presence of an obtuse angle in a triangle affect the measures of the other angles?
  • When a triangle has one obtuse angle, the remaining two angles must both be acute to satisfy the rule that all three interior angles sum to 180 degrees. Since an obtuse angle exceeds 90 degrees, this limitation means that each of the other two angles must be less than 90 degrees. Consequently, this leads to the classification of such triangles as obtuse triangles.
• In what ways can understanding obtuse angles contribute to solving problems related to measuring angles and segments?
  • Understanding obtuse angles is essential in solving various geometry problems as it allows you to recognize relationships between different angles. For instance, knowing that an obtuse angle measures more than 90 degrees helps in identifying complementary and supplementary relationships with other angles. This knowledge aids in calculations involving unknown angles and determining segment lengths using geometric principles.
• Evaluate how the concept of obtuse angles can enhance our understanding of broader geometric principles and their applications in real-life scenarios.
  • The concept of obtuse angles deepens our comprehension of geometric principles by illustrating how different angle types interact within shapes. In practical terms, understanding obtuse angles is crucial for fields like architecture and engineering where such angles affect design and structural integrity. For example, roof designs often incorporate obtuse angles to facilitate water drainage or aesthetics, demonstrating the real-world relevance of this geometric concept.

Related terms

Acute Angle: An acute angle is an angle that measures less than 90 degrees.

Right Angle: A right angle is an angle that measures exactly 90 degrees.

Supplementary Angles: Supplementary angles are two angles that add up to 180 degrees.