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Adding and Subtracting Angles

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Angles are sections of a full circle. A full circle can be divided into angles of many sizes. If all of the angles are placed together without overlapping, their total will be 360°. Angles can be added together to make larger angles. Angles can be divided into smaller angles.

Learning Outcomes

By the end of this lesson, your children will be able to use addition and subtraction to find the measure of an unknown angle.

Warm Up

Angles are sections of a full circle. They are measured in degrees. Two adjacent angles (angles that are next to each other without overlapping) can be added together to make a larger angle.

If a large angle is made up of two smaller angles, the measurement of one of the smaller angles can be subtracted from the measurement of the large angle to find the measurement of the second small angle.

Using an algebraic equation with a variable to stand for an unknown angle measurement is a good strategy, especially if some of the angle measurements are known.

In this lesson you will observe how the measurements of angles can be added and subtracted to find a missing angle measurement, and use equations to solve similar problems.

Pre-assessment worksheet

Have your children take the Pre-Test below to see if they are ready for this lesson. If they get 7 or less correct, review degrees in a circle with them before continuing on to the lesson.

Main Lesson: Adding and Subtracting to Find Unknown Angles

Now that you have had some practice adding adjacent angles together to make a larger angle, it's time to work on finding the measure of an unknown angle by using the known measures. Let's look at an example:

example of two angles adding up to 107 degrees

If angle ABD = 107°, what is the measure of angle ABC?

Let's start with what we know.

Angle ABC + Angle CBD = Angle ABD

Plug in the known:

Use the inverse operation to isolate the variable
n + 37°

-37 
=107°

-37 
  n = 70°

So Angle ABC = 70°

Let’s practice with another example:

two angles one of which is 44 degrees

If angle RSU = 62 °, what is the measure of angle TSU?

Let’s start with what we know.

Angle RST + Angle TSU = Angle RSU

We plug in what we know, then isolate the variable using the inverse operation. To keep it balanced, we subtract the same amount from the other side of the equation.  44° + n

-44 
=62°

 -44
  = 18°

So Angle TSU = 18 °

Now try the same skill in the form of a word problem. Follow the reminders below and then check your answer.

Problem:

Angle MOP measures 126°. It is divided into two smaller angles:

Angle MON measures 58°.

The measure of the third angle, Angle NOP is unknown.

If Angle MON + Angle NOP = Angle MOP, what is the measure of Angle NOP?

Solution:

If no drawing is provided with a problem, and you need one to help you understand it, don't be afraid to make your own.

Unpack the problem: pay attention to the information you are given, and what you are being asked to solve.

Angle MON + Angle NOP = Angle MOP

Write an equation, plugging in the information you know.

58°+ n = 126°

Isolate the variable using the inverse operation.

Keep it balanced. Do the same thing on the other side of the equation.

 58°+ n

-58 
=126°

 -58
n  = 68°
The measure of angle NOP is 68°

Recap

  • Angles can be added together to make larger angles.
  • If the measure of one of the smaller angles is unknown, the measure of the large angle and the known small angle can be used to find it.
  • An equation with a variable can be used.
  • When the measure of the unknown angle is found, the two small angles added together should equal the large angle.

Test Questions

Review the above recap points with your children and then print out the Post Test that follows.

At least 5 out of 6 correct will show that your children are ready to go on to the next lesson.

 

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