Types of Aangles (Right, Acute, Obtuse, Flat): Identifying and defining elements

To solve this problem, we'll follow these steps:

• Step 1: Identify the angle measure provided.
• Step 2: Match the angle measure to the corresponding type of angle.
• Step 3: Choose the correct type of angle from the multiple-choice options.

Let's break down the process:

Step 1: The problem specifies that $\angle \text{ABC} = 90^\circ$.

Step 2: Recall the definitions of angle types. A right angle is defined as an angle that measures exactly 90 degrees.

Step 3: Out of the provided choices, select the one that represents a right angle.
- Right angle: $\angle = 90^\circ$ (Correct Choice)
- Acute angle: $\angle < 90^\circ$
- Obtuse angle: $\angle > 90^\circ$ and $\angle < 180^\circ$
- Flat angle: $\angle = 180^\circ$

Thus, the conclusion is that $\angle \text{ABC}$ is a Right angle.

To determine the type of angle $\angle \text{ABC}$, we will consider the following:

• Step 1: Observe the positions of points A, B, and C, which are depicted in the diagram as lying on a straight line.
• Step 2: Recognize that when three points lie on a straight line and a central point (B here) is between two others (A and C), it forms a flat angle.
• Step 3: Recall that a flat angle is defined as an angle that measures $180^\circ$, which is the total rotation a line undergoes around a single point.

Visual inspection of the diagram confirms that points A, B, and C create a straight line. Hence, the angle $\angle \text{ABC}$ must be a flat angle.

Therefore, the angle $\angle \text{ABC}$ is a flat angle.

To determine what kind of angle $\angle \text{ABC}$ is, let's examine the given information: the angle is less than $90^\circ$.

• Step 1: Recall the types of angles based on their measurements:
• An acute angle measures less than $90^\circ$.
• A right angle measures exactly $90^\circ$.
• An obtuse angle measures greater than $90^\circ$ but less than $180^\circ$.
• A flat angle measures exactly $180^\circ$.
• Step 2: Match the given information with these definitions.

Since $\angle \text{ABC}$ measures less than $90^\circ$, it fits the definition of an acute angle.

Therefore, the angle $\angle \text{ABC}$ is an acute angle.

A right angle is equal to 90 degrees.

In diagrams (a) and (c), we can observe that the angle symbol is a symbol representing an angle that equals 90 degrees.

By definition, an obtuse angle is an angle that is greater than 90 degrees. We can observe that in one drawing there is an angle of 90 degrees and therefore it is not an obtuse angle, the other two angles are less than 90 degrees meaning they are also not obtuse, they are acute angles.

Therefore, none of the answers is correct.

The definition of an acute angle is an angle that is smaller than 90 degrees.

Since an angle that equals 90 degrees is a right angle, the statement is true.

One of the properties of a rectangle is that all its angles are right angles.

Therefore, it is not possible for an angle to be acute, that is, less than 90 degrees.

Let's note in which of the triangles angle B forms a right angle, meaning an angle of 90 degrees.

In answers C+D, we can see that angle B is smaller than 90 degrees.

In answer A, it is equal to 90 degrees.