A protractor is a tool used to measure angles, but having one is only sometimes necessary. There are a few different ways to measure angles without a protractor.

**One way to measure angles without a protractor is to use a ruler and a compass.**

To do this, follow these steps:

- Draw a line segment on a piece of paper.

- Place the compass point at one end of the line segment and draw an arc that intersects the line segment at a point.

- Place the ruler on the line segment and measure the distance between the end of the line segment and the point where the arc intersects the line segment.

- Use a calculator to find the arctangent of the space you measured. The arctangent will be the angle in degrees.

**Another way to measure angles without a protractor is to use a right triangle.**

To do this, follow these steps:

- Draw a right triangle on a piece of paper.

- Measure the lengths of the two legs of the right triangle.

- Use a calculator to find the arctangent of the length of one leg divided by the size of the other leg. The arctangent will be the angle in degrees.

**Finally, you can use a smartphone to measure angles without a protractor.**

There are several different apps available that can measure angles. To use an app to measure an angle, point your phone at the rise, and the app will display the angle in degrees.

**Here are some additional tips for measuring angles without a protractor:**

- Ensure that the line segment or right triangle you use is accurately drawn.
- Use a ruler or compass that is accurate to within a millimeter.
- Be careful when using a calculator to find the arctangent. Make sure that you are entering the correct values and that you are using the proper function.

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**Here are some FAQs:**

**Which method is the most accurate?**

The most accurate method for measuring angles without a protractor is to use a right triangle and a calculator. However, the ruler and compass method can also be valid if the line segment is accurately drawn and the ruler and compass are accurate within a millimeter.

**What if I don’t have a calculator?**

If you don’t have a calculator, you can still use the ruler and compass method to measure angles, but the results will not be as accurate. You can also use a smartphone app to measure angles.

**What if I don’t have a ruler or compass?**

If you need a ruler or compass, you can still use the suitable triangle method to measure angles, but it will be more difficult. It would help if you used a straight edge and a piece of string to draw the right triangle.

**How can I use a smartphone app to measure angles?**

To use a smartphone app to measure angles, point your phone at the rise, and the app will display the angle in degrees. Most smartphone apps also allow you to save and share your measurements.

**When would I need to measure angles without a protractor?**

You may need to measure angles without a protractor if you do not have access to a protractor or if you need to measure an angle that is too large or too small to be measured accurately with a protractor.

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