d. None of these 2. Classify the angle shown on the right. a. right b. acute c. obtuse d. straight
The Correct Answer and Explanation is:
The correct answer is b. acute.
Explanation:
To classify the angle shown in the image, we must determine its type based on its measurement. Angles are typically categorized into four main types: acute, right, obtuse, and straight. Understanding the definition of each type is key to correctly identifying the angle.
- Right Angle: A right angle measures exactly 90 degrees. It forms a perfect corner, like the corner of a square or a book. It is often indicated by a small square symbol at the vertex, although not always.
- Acute Angle: An acute angle is an angle that measures less than 90 degrees. It appears “sharper” or smaller than a right angle.
- Obtuse Angle: An obtuse angle measures more than 90 degrees but less than 180 degrees. It is wider or more open than a right angle.
- Straight Angle: A straight angle measures exactly 180 degrees, forming a perfectly straight line.
Now, let’s analyze the angle in the image, which can be named ∠DEF, with its vertex at point E. To classify it, we can visually compare it to a 90-degree right angle. If we imagine a perfectly vertical line and a perfectly horizontal line meeting at vertex E, they would form a right angle.
In the given figure, the ray EF is nearly vertical. However, the ray ED is not horizontal; instead, it points upwards and to the left. The opening between ray ED and ray EF is clearly smaller than the 90-degree opening of a right angle. Because the measure of ∠DEF is less than 90 degrees, it fits the definition of an acute angle.
Therefore, the other options are incorrect. It is not a right angle because it doesn’t form a perfect 90-degree corner. It is not an obtuse angle because it is smaller, not wider, than a right angle. Finally, it is not a straight angle because the two rays do not form a straight line. The correct classification for the given angle is acute.
