Ch. 1 - Angles and the Trigonometric Functions

Blitzer3rd EditionTrigonometryISBN: 9780137316601Not the one you use?Change textbook

Blitzer 3rd Edition

Ch. 1 - Angles and the Trigonometric Functions

Problem 1

Chapter 1, Problem 1

In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 135°

Verified step by step guidance

Recall the definitions of angle classifications: an acute angle is between 0° and 90°, a right angle is exactly 90°, an obtuse angle is between 90° and 180°, and a straight angle is exactly 180°.

Look at the given angle measure, which is 135°.

Compare 135° to the ranges defined: since 135° is greater than 90° but less than 180°, it falls into the obtuse angle category.

Therefore, classify the angle 135° as an obtuse angle based on the comparison.

Summarize: 135° is an obtuse angle because it lies between 90° and 180°.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Angle Measurement in Degrees

Angles are measured in degrees, representing the amount of rotation from one ray to another around a common vertex. A full circle is 360°, a straight angle is 180°, and smaller angles are fractions of this rotation.

Classification of Angles

Angles are classified based on their measure: acute angles are less than 90°, right angles are exactly 90°, obtuse angles are greater than 90° but less than 180°, and straight angles are exactly 180°.

Comparing Angle Measures

To classify an angle, compare its degree measure to the standard angle categories. For example, 135° is greater than 90° but less than 180°, so it is classified as an obtuse angle.

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