Problem Analysis:
The image provides a table categorizing different types of angles based on their measures. The task is to understand and explain the classification of angles into four categories:
Acute angle,
Right angle,
Obtuse angle, and
Reflex angle. Each category is defined by a specific range of angle measures, and diagrams are provided to illustrate each type.
Solution Explanation:
#### 1.
Acute Angle
-
Definition: An acute angle is an angle whose measure is greater than \(0^\circ\) but less than \(90^\circ\).
\[
0^\circ \leq x < 90^\circ
\]
-
Diagram: The diagram shows a small, sharp angle, which visually represents an angle that is less than a right angle.
-
Key Feature: Acute angles are "sharp" and smaller than a right angle.
#### 2.
Right Angle
-
Definition: A right angle is an angle whose measure is exactly \(90^\circ\).
\[
x = 90^\circ
\]
-
Diagram: The diagram shows two perpendicular lines forming a square corner, which is the characteristic shape of a right angle.
-
Key Feature: Right angles are often marked with a small square in the corner to indicate the \(90^\circ\) measure.
#### 3.
Obtuse Angle
-
Definition: An obtuse angle is an angle whose measure is greater than \(90^\circ\) but less than or equal to \(180^\circ\).
\[
90^\circ < x \leq 180^\circ
\]
-
Diagram: The diagram shows a wider angle that is larger than a right angle but less than a straight line.
-
Key Feature: Obtuse angles are "blunt" and larger than a right angle but smaller than a straight angle.
#### 4.
Reflex Angle
-
Definition: A reflex angle is an angle whose measure is greater than \(180^\circ\) but less than or equal to \(360^\circ\).
\[
180^\circ < x \leq 360^\circ
\]
-
Diagram: The diagram shows an angle that is larger than a straight line but less than a full rotation.
-
Key Feature: Reflex angles are the "larger counterparts" of the corresponding acute or obtuse angles when measured in the opposite direction.
Summary of Angle Types:
-
Acute Angle: \(0^\circ \leq x < 90^\circ\)
-
Right Angle: \(x = 90^\circ\)
-
Obtuse Angle: \(90^\circ < x \leq 180^\circ\)
-
Reflex Angle: \(180^\circ < x \leq 360^\circ\)
Final Answer:
\[
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{Type of Angle} & \text{Description} & \text{Diagram} \\
\hline
\text{Acute angle} & 0^\circ \leq x < 90^\circ & \text{(Small, sharp angle)} \\
\hline
\text{Right angle} & x = 90^\circ & \text{(Perpendicular lines, square corner)} \\
\hline
\text{Obtuse angle} & 90^\circ < x \leq 180^\circ & \text{(Wider than right angle, less than straight line)} \\
\hline
\text{Reflex angle} & 180^\circ < x \leq 360^\circ & \text{(Larger than straight line, less than full rotation)} \\
\hline
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of angles of math.
