How to Measure Angles
Learn to measure angles precisely with protractors. Master the techniques professionals use for accurate angle measurement in geometry and real-world applications.
Understanding Angle Types
Acute Angle
Less than 90 degrees. Sharp and narrow angles.
Right Angle
Exactly 90 degrees. Forms a perfect square corner.
Obtuse Angle
Greater than 90° but less than 180°. Wide, open angles.
Straight Angle
Exactly 180 degrees. Forms a straight line.
Step-by-Step Measurement Guide
Identify the Angle
Locate the angle you want to measure. An angle is formed by two rays (lines) that meet at a point called the vertex.
Key Terms:
- • Vertex: The point where two lines meet
- • Rays: The two lines that form the angle
- • Arc: The curved space between the rays
Position the Protractor
Place the center point (crosshairs) of the protractor exactly on the vertex of the angle. This is the most critical step for accurate measurement.
🎯 Alignment Tip:
The small hole or crosshairs in the center of your protractor should be directly over the vertex point. Take your time to get this exactly right.
Align the Baseline
Rotate the protractor so that the baseline (0° line) aligns perfectly with one of the angle's rays. This ray becomes your reference line.
Left-to-Right:
If measuring from left to right, use the outer scale (usually at the bottom).
Right-to-Left:
If measuring from right to left, use the inner scale (usually at the top).
Read the Scale
Look at where the second ray intersects the protractor scale. Read the number at that intersection point. This is your angle measurement.
✅ Reading Tips:
- • Use the same scale you aligned with (inner or outer)
- • Read from the 0° starting point
- • Estimate between marks for greater precision
- • Always include the degree symbol (°)
Common Mistakes to Avoid
Wrong Scale Reading
Using the inner scale when you aligned with the outer scale (or vice versa) gives incorrect measurements.
Misaligned Center
Not placing the protractor's center exactly on the vertex leads to significant measurement errors.
Confusing Complementary
Reading the complement (180° - angle) instead of the actual angle, especially with obtuse angles.
Parallax Error
Looking at the scale from an angle instead of directly above can cause misreadings.
Special Measurement Cases
Reflex Angles
Angles greater than 180°. Measure the smaller angle first, then subtract from 360°.
Reflex = 360° - measured angle
Very Small Angles
For angles smaller than 10°, use a larger protractor or digital tools for better precision.
Consider using minutes (') and seconds (") for very precise measurements.
Angles in Shapes
When measuring angles inside shapes, extend the lines if needed to make measurement easier.
Triangle angles always sum to 180°. Use this to check your measurements.
Master Angle Measurement
Practice measuring angles with our interactive virtual protractor. Get instant feedback and perfect your technique.
Try Virtual Protractor