**Introduction to Measuring Angles**

**Lesson Summary**

This lesson focuses on using the protractor to measure and draw angles. You will also add and subtract angle measures.

**A**n instrument called a *protractor* can be used to find the measure of degrees of an angle. Most protractors have two scales, one reading from left to right, and the other from right to left. Estimating whether an angle is acute, right, obtuse, or straight before measuring will help you choose the correct scale. Here is an example of a protractor:

Carefully line up your protractor by placing the center point of the protractor scale on the vertex of the angle, which is the place where both sides of the angle meet. If the sides of the angle do not reach the scale, extend them. Choose the scale that has zero at one side of the angle. Read the measure of the angle. Check to see if your measurement and estimate agree. When measuring an angle, it is not necessary to have one of the rays passing through zero on the protractor scale. The angle could be measured by subtracting the smaller measurement from the larger one. Putting the ray on zero simply makes the counting easier.

**Drawing Angles**

You can use a protractor to draw an angle of a given size. First, draw a ray and place the center point of the protractor on the endpoint of the ray. Align the ray with the base line of the protractor. Locate the degree of the angle you wish to draw. Make a dot at that point and connect it to the endpoint of the ray.

The resulting angle will have the correct degree of measurement:

**Adding and Subtracting Angle Measures**

The following figures suggest that you can add and subtract angle measures:

*Adjacent* angles are two angles in the same plane that have the same vertex and a common side but do not have any interior points in common.

In the previous figure, 1 and 2 are adjacent angles. Angles 1 and *XYZ* are not adjacent.

Use a protractor to measure 1, 2, and *XYZ*. What relationship do you notice among the measures of the three angles? You should find that the measure of 1 plus the measure of 2 equals the measure of *XYZ*. The letter *m* is used before the angle symbol to represent the word *measure*. For example, *m1 + m2 = mXYZ*. If you draw another pair of adjacent angles and measure the angles, will the relationship be the same? Try it and see.

**Examples: **

Find the measure of each angle.

*m*2 = 75°

*mRSW* = ___

*m*1 + *m*2 = *mRSW*

*mRSW* = 115°

*mGEF* = 145°

*mDEF* = ___

*mDEG + mGEF = mDEF*

*mDEF* = 180°

*m*1 = 40°*mDEG*= 35°

Practice problems for these concepts can be found at: Measuring Angles Practice Questions.

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