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Chapter 1: Problem 6

An angle with a measure of \(90^{\circ}\) is a(n) __________ angle.

Short Answer

Expert verified
An angle with a measure of 90 degrees is a right angle.

Step by step solution

01

Understanding Angles

First, review the different types of angles based on their measures. An acute angle measures less than 90 degrees, an obtuse angle measures more than 90 degrees but less than 180 degrees, and a right angle measures exactly 90 degrees.
02

Identify the Angle

Given the measure of the angle is 90 degrees, determine which category it falls into. According to the definitions, a right angle is precisely 90 degrees.
03

Conclusion

Conclude that an angle measuring exactly 90 degrees is known as a right angle.

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Key Concepts

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

Types of Angles
Angles are essential building blocks in geometry and appear in various shapes and structures. We classify angles based on their measures. Here are the primary types:
  • Acute Angle: An acute angle measures less than 90 degrees. It is sharp and narrow.
  • Right Angle: A right angle measures exactly 90 degrees. It looks like the corner of a square or rectangle.
  • Obtuse Angle: An obtuse angle measures more than 90 degrees but less than 180 degrees. It is wider than a right angle.
  • Straight Angle: A straight angle measures exactly 180 degrees. It forms a straight line.
Recognizing these types can help in understanding shapes and solving various geometric problems more efficiently.
Angle Measures
Understanding how to measure angles is crucial in geometry. The unit of measurement for angles is degrees (掳). Here's a breakdown of common angle measures:
  • 0掳: This represents a null angle, where the two lines overlap completely.
  • 90掳: This is a right angle, creating a perfect 'L' shape.
  • 180掳: Known as a straight angle, it forms a straight line.
  • 360掳: This represents a full rotation, forming a complete circle.
Measuring angles with a protractor is a common practice. Place the midpoint of the protractor at the angle's vertex and read the degree measurement where the lines intersect the scale. Identifying the measures accurately helps in constructing shapes and solving for missing angles.
Right Angle Definition
A right angle is one of the most frequently encountered angles in geometry. Defined as an angle that measures exactly 90 degrees, it is fundamental in various fields, such as construction and design. Here's what you need to know:
  • Appearance: A right angle looks like the corner of a square or rectangle. It creates a perfect 'L' shape.
  • Symbol: Often represented by a small square in the corner of the angle to indicate 90 degrees.
  • Usage: Engineers and architects rely on right angles to ensure buildings and structures are stable and correctly aligned.
Understanding and identifying right angles is essential for studying and working in any field involving geometric shapes and designs.

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Most popular questions from this chapter

True or false? Do not use a calculator. $$ \sin \left(91^{\circ}\right)=-\sin \left(89^{\circ}\right) $$

Find the equation of a vertical line through \((\pi, 0)\).

Find the measure in radians of the smallest positive angle that is coterminal with each given angle. For angles given in terms of \(\pi\) express the answer in terms of \(\pi\). Otherwise, round to the nearest hundredth. $$ -\frac{7 \pi}{6} $$

Find the exact value of each expression for the given value of \(\theta\) Do not use a calculator. $$ \sin (\theta / 2) \text { if } \theta=2 \pi / 3 $$

Solve each problem. If \(\sec \alpha=10 / 3,\) then what is \(\cos \alpha ?\)
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