Lesson 1 Central and Inscribed Angles and Arcs-worksheet.pdf ... - Free Printable

Let’s solve this step by step.

We are given a set of equations with shapes representing numbers. Our goal is to find the value of each shape and then compute the final expression.

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Step 1: Look at the first equation

🟥 + 🟥 = 10
That means two red squares equal 10.
So, one red square = 10 ÷ 2 = 5

✔ Red Square (🟥) = 5

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Step 2: Second equation

🟥 × 🔵 = 15
We know 🟥 = 5, so:

5 × 🔵 = 15
→ 🔵 = 15 ÷ 5 = 3

✔ Blue Circle (🔵) = 3

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Step 3: Third equation

🔵 + 🟩 = 8
We know 🔵 = 3, so:

3 + 🟩 = 8
→ 🟩 = 8 - 3 = 5

✔ Green Triangle (🟩) = 5

Wait — that’s the same as the red square? Let’s keep going and check if that makes sense.

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Step 4: Fourth equation

🟩 × ⚪ = 20
We have 🟩 = 5, so:

5 × ⚪ = 20
→ ⚪ = 20 ÷ 5 = 4

✔ White Circle (⚪) = 4

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Step 5: Fifth equation

⚪ + 🟨 = 9
We have ⚪ = 4, so:

4 + 🟨 = 9
→ 🟨 = 9 - 4 = 5

✔ Yellow Diamond (🟨) = 5

Again, another 5? That’s okay — different shapes can have same values unless told otherwise.

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Step 6: Sixth equation

🟨 × 🟦 = 30
We have 🟨 = 5, so:

5 × 🟦 = 30
→ 🟦 = 30 ÷ 5 = 6

✔ Blue Square (🟦) = 6

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Now, let’s look at the final expression we need to solve:

> 🟥 + 🔵 × 🟩 + ⚪ + 🟨 + 🟦

But wait — order of operations matters! Multiplication comes before addition.

So rewrite it with parentheses for clarity:

= 🟥 + (🔵 × 🟩) + ⚪ + + 🟦

Plug in the values:

= 5 + (3 × 5) + 4 + 5 + 6

Calculate inside parentheses first:

= 5 + 15 + 4 + 5 + 6

Now add left to right:

5 + 15 = 20
20 + 4 = 24
24 + 5 = 29
29 + 6 = 35

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Final Answer:
35