Learn about angles through these example problems with detailed step-by-step solutions.
Example 1: Angle Classification
Classify the angle measuring 75°.
Step 1: Recall the definitions of different types of angles based on their measure.
Step 2: An acute angle is less than 90°.
Step 3: A right angle is exactly 90°.
Step 4: An obtuse angle is greater than 90° but less than 180°.
Step 5: A straight angle is exactly 180°.
Step 6: The given angle is 75°. Since $75^\circ < 90^\circ$, it fits the definition of an acute angle.
Step 7: Therefore, the angle measuring 75° is an acute angle.
Example 2: Measuring an Angle (requires diagram or visual context not possible in pure text)
Imagine an angle formed by two rays meeting at a point. One ray goes horizontally to the right, and the other ray goes upwards and slightly to the right.
Measure this angle using a protractor.
Step 1: Place the vertex of the angle at the center point of the protractor (usually marked with a hole or a cross).
Step 2: Align the base line of the protractor with one of the rays of the angle, making sure the 0° mark is on the ray.
Step 3: Read the measure on the protractor scale where the other ray crosses the scale. Use the correct scale (inner or outer) depending on which 0° mark you aligned with the first ray.
Step 4: For the described angle, the measure is typically less than 90°. (Note: A diagram would be necessary for an exact measurement).
Step 5: Let's assume the angle measures 40°. So, the angle measures 40°.
Example 3: Drawing Angles
Draw an angle of 120° using a protractor.
Step 1: Draw a ray starting from a point. This point will be the vertex of the angle.
Step 2: Place the protractor's center on the vertex and align the 0° line with the ray you just drew.
Step 3: Find the 120° mark on the protractor scale and make a small dot. (Remember to use the correct scale - if your ray is aligned with the 0° on the right, use the inner scale; if it's on the left, use the outer scale).
Step 4: Remove the protractor and draw a second ray from the vertex through the dot you made.
Step 5: The angle formed by the two rays is a 120° angle. It should look like an obtuse angle.
Practice Mode
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Related Concepts
Explore these related mathematical concepts to deepen your understanding of angles.
Point, Ray, Line Segment
Basic geometric elements that form angles. An angle is formed by two rays sharing a common endpoint (vertex).
Vertex
The common endpoint where the two rays of an angle meet.
Arms (or Sides) of an Angle
The two rays that form an angle.
Protractor
A mathematical instrument used to measure or draw angles.
Degree
The standard unit of measurement for angles, denoted by the symbol (°).
