Measurement and Types of Angles

An angle is formed when two lines meet at a point called the vertex.

• Angles are measured in degrees (°), representing the rotation between the two lines.
• Usually, angles are measured in the counterclockwise direction.

Angles are classified based on their size:

• Acute Angle: Less than $90^\circ$
• Right Angle: Exactly $90^\circ$
• Obtuse Angle: $90^\circ < \alpha < 180^\circ$
• Straight Angle: Exactly $180^\circ$
• Reflex Angle: $180^\circ < \alpha < 360^\circ$
• Full Angle: Exactly $360^\circ$, a complete turn

To measure the size of an angle correctly, follow these 3 steps:

1. Place the protractor: Align the center of the protractor with the vertex of the angle.
2. Align the zero line: Ensure one arm of the angle is lined up with the zero mark on the protractor.
3. Read the scale: Observe where the other arm crosses the number scale to determine the angle’s measurement.

Example:

• Here, one arm of the angle is at 0°, and the other crosses at 130° (or 50° on the opposite scale).
• Since we know this is an obtuse angle ($90^\circ < \alpha < 180^\circ$), we take the larger value and confirm that the angle is 130°.

When an angle is greater than 180°, we measure the opposite angle first and subtract it from 360° to find the correct angle.

Example:

1. Instead of measuring the large angle directly, we first measure the smaller angle, which is 140°.
2. Since a full circle is 360°, we subtract:

$$\text{Angle} = 360^\circ – 140^\circ= 220^\circ$$

Thus, this angle is 220°, which is a reflex angle.

To construct a 40° angle, follow these 4 steps:

1. Draw the first arm: Start by drawing a straight, horizontal line. Choose a point on this line to be the vertex of the angle.
2. Place the protractor: Align the center of the protractor exactly on the vertex. Ensure the zero line aligns with the first arm.
3. Mark the angle: Locate 40° on the protractor’s scale and mark the spot.
4. Draw the second arm: Use a ruler to draw a line from the vertex to the 40° mark.

And that’s it! You’ve constructed a 40° angle.