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Chapter 5: Problem 5

An angle with a measure between \(90^{\circ}\) and \(180^{\circ}\) is an ________ angle.

Short Answer

Expert verified
obtuse

Step by step solution

01

Identify the range of the angle

Angles with measures between \(90^{\text{掳}}\) and \(180^{\text{掳}}\) lie between a right angle and a straight angle.
02

Determine the specific type of angle

An angle greater than \(90^{\text{掳}}\) and less than \(180^{\text{掳}}\) is identified as an obtuse angle.
03

Verify the definition

Check the definitions to confirm: An acute angle is between \(0^{\text{掳}}\) and \(90^{\text{掳}}\), a right angle is exactly \(90^{\text{掳}}\), and a straight angle is exactly \(180^{\text{掳}}\). The correct term for an angle between \(90^{\text{掳}}\) and \(180^{\text{掳}}\) is obtuse.

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Key Concepts

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

Obtuse Angle
An obtuse angle is a type of angle that measures greater than 90掳 but less than 180掳. It is wider than a right angle and narrower than a straight angle. These angles are more expansive and can be visually identified because they 'open' more than a right angle, but they do not form a straight line.
Here are some characteristics of an obtuse angle:
  • Measures between 90掳 and 180掳
  • Is greater than a right angle
  • Is less than a straight angle
Obtuse angles are common in various geometric shapes and everyday objects, making them an essential concept to understand.
Angle Measurement
Angle measurement helps us to determine the size of an angle, typically in degrees (掳). An angle is formed by two rays that share a common endpoint, called the vertex. The amount of turn between each arm is measured in degrees.
Here are some key points about angle measurement:
  • The smallest angle is 0掳, which represents no turn at all.
  • Angles are measured using a protractor, a tool that helps to measure angles accurately.
  • The full turn around a point is 360掳.
Understanding how to measure angles is critical in various applications, from constructing buildings to creating art.
Right Angle
A right angle is an angle that measures exactly 90掳. It is one of the foundational angles in geometry and can be easily recognized by its characteristic 'L' shape.
Key attributes of a right angle:
  • Measures exactly 90掳
  • Forms a perfect 'L' shape
  • Is used as a reference point for other angles
Recognizing and constructing right angles are essential skills in both basic and advanced geometry.
Straight Angle
A straight angle is an angle that measures exactly 180掳. It is formed when the two rays forming the angle point in exactly opposite directions, creating a straight line.
Notable features of a straight angle:
  • Measures exactly 180掳
  • Forms a straight line
  • Is equal to the sum of two right angles (90掳 + 90掳)
Straight angles are fundamental in understanding line geometry and the concept of linearity in math.
Acute Angle
An acute angle is a type of angle that measures less than 90掳. These angles are smaller and sharper compared to right and obtuse angles.
Distinctive characteristics of acute angles:
  • Measures between 0掳 and 90掳
  • Is smaller than a right angle
  • Commonly found in many geometric shapes
Acute angles are significant because they are present in various natural and man-made structures, making them an essential aspect of everyday geometry.

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