In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight.87.177°

Verified step by step guidance

1. Understand the classification of angles: 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°.
2. Identify the given angle measure: 87.177°.
3. Compare the given angle measure to the classifications: Check if 87.177° is less than 90°, equal to 90°, greater than 90° but less than 180°, or equal to 180°.
4. Determine the classification based on the comparison: Since 87.177° is less than 90°, it falls into the category of acute angles.
5. Conclude that the angle is classified as an acute angle.

Key Concepts

Types of Angles

Angles can be classified into four main types based on their measures: acute angles (less than 90°), right angles (exactly 90°), obtuse angles (greater than 90° but less than 180°), and straight angles (exactly 180°). Understanding these classifications is essential for determining the nature of any given angle.

Angle Measurement

Angles are measured in degrees, with a full rotation around a point equating to 360°. The measurement of an angle helps in identifying its classification. For example, an angle measuring 87.177° is less than 90°, indicating it is acute.

Visual Representation of Angles

Visualizing angles can aid in their classification. Drawing angles or using protractors can help students see the differences between acute, right, obtuse, and straight angles. This visual approach reinforces understanding and assists in accurately categorizing angles based on their measures.