Additive Angles

Contributor: Ashley Nail. Lesson ID: 13884

Did you know that sharing your food with siblings can test your geometry skills? In this lesson, you will find the unknown angle by decomposing a bigger angle into smaller angles.


Geometry, Measurement and Data

learning style
personality style
Lion, Otter, Beaver, Golden Retriever
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

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Amelia has a slice of watermelon that she wants to share with her brother and sister. She is going to ask her dad to slice it into three parts. Amelia’s brother wants a big piece, and her sister wants a small piece. Amelia wonders how big her remaining piece will be.

watermelon split three ways

Amelia’s dad hands her a protractor but tells her she can only measure her sister’s and brother’s pieces. She cannot measure her own piece!

  • How will that help her?
  • How can Amelia find out how big a piece of watermelon she will have after she shares with her brother and sister?

Before Amelia figures out how much watermelon she will eat, let’s look at another slice she shared with her dad.

watermelon sliced two ways

Let’s redraw this picture as a diagram with measurements of angles:

diagram 1

We know Amelia’s piece of watermelon was 55° and that the entire piece of watermelon was 130°. We need to figure out the measurement of Amelia’s dad’s piece of watermelon.

We can do this by decomposing angles, which is just a fancy way of saying "breag the angles into smaller angles."

Let’s look more closely at what we already know. The big angle is decomposed into two smaller angles.

The big angle measures 130°. We can name this angle ∠DAB:

diagram 2

Amelia’s angle measures 55°. We can name this angle ∠DAC:

diagram 3

Dad’s angle has an unknown measurement. We can still name this angle ∠CAB:

diagram 4

Now, we’re ready to find the unknown measurement!

We know that Amelia’s watermelon slice and her dad’s watermelon slice together equal the entire piece of watermelon. Let’s write that as an equation:

diagram 5

We know we can add the two angles together because the bigger angle is decomposed. The smaller angles inside the bigger angle are adjacent.

Remember: adjacent angles are angles that share a side or line segment. For example, Amelia’s angle shares a side with her dad’s angle. They share the line segment AC.

Now, use what we know to plug information into our equation. We know the total measurement of ∠DAB is 130°. We also know ∠DAC is 55°:

diagram 6

  • What can we add to 55 to equal 130?

In order to find the unknown measurement, we need to subtract 55 from 130:

130 - 55 = 75

Let’s double check our work by plugging 75 in as the unknown measurement:

diagram 7

It works!

Now we know Amelia’s dad ate a slice of watermelon that measured 75°.

  • But what about the watermelon slice Amelia shared with her brother and sister?
  • What was the measurement of her piece?

You might need some more practice before you help Amelia solve her problem!

Click “next” to visit the Got It? section to practice working with decomposing angles!

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