Find the measure of interior angles for each regular polygon and calculate the sum of the interior angles.

Let’s solve this step by step.

We are given regular polygons — that means all sides and angles are equal. We need to find:
1. The measure of each interior angle.
2. The sum of all interior angles for each polygon.

There’s a simple formula for the sum of interior angles of any polygon:

> Sum = (n - 2) × 180°

Where n is the number of sides.

Then, since it’s a *regular* polygon, we divide that sum by n to get each interior angle:

> Each interior angle = Sum ÷ n

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Let’s go shape by shape.

1. Triangle (already done as example)

- Sides: 3
- Sum = (3 - 2) × 180° = 1 × 180° = 180°
- Each angle = 180° ÷ 3 = 60° → matches the example!

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2. Square (4 sides)

- Sum = (4 - 2) × 180° = 2 × 180° = 360°
- Each angle = 360° ÷ 4 = 90°

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3. Pentagon (5 sides)

- Sum = (5 - 2) × 180° = 3 × 180° = 540°
- Each angle = 540° ÷ 5 = 108°

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4. Hexagon (6 sides)

- Sum = (6 - 2) × 180° = 4 × 180° = 720°
- Each angle = 720° ÷ 6 = 120°

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5. Heptagon (7 sides)

- Sum = (7 - 2) × 180° = 5 × 180° = 900°
- Each angle = 900° ÷ 7 ≈ 128.57°
*(But let’s keep it exact: 900/7 degrees)*

Wait — actually, in most school worksheets, they expect you to write the exact fraction or rounded decimal? Let me check: 900 ÷ 7 = 128.571... So we can write ≈128.6° if rounding to one decimal, but maybe better to leave as fraction? Actually, no — for regular polygons, sometimes they accept decimals. But let’s see what’s standard.

Actually, looking at the triangle example, they used whole numbers. For heptagon, it’s not a whole number. But we’ll calculate exactly.

Hold on — let me double-check my math.

(7-2)=5 → 5×180=900 → 900÷7 = 128.571428... so yes.

But perhaps the worksheet expects us to write the exact value? Or maybe I made a mistake?

No — it’s correct. Some polygons don’t have whole-number interior angles.

But wait — let me confirm with known values:

Yes, regular heptagon interior angle is approximately 128.57°.

We’ll write it as 128.57° (rounded to two decimals) or leave as fraction? Since the problem didn’t specify, and the triangle was exact, maybe we should write the exact fractional form? But that might be too advanced.

Actually, in middle school, they often round to nearest tenth or just leave as calculation.

But let’s look ahead — octagon will also not be whole number? Wait no — octagon is 8 sides.

Wait — let’s do octagon first.

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6. Octagon (8 sides)

- Sum = (8 - 2) × 180° = 6 × 180° = 1080°
- Each angle = 1080° ÷ 8 = 135° → nice whole number!

So back to heptagon — 900 ÷ 7 = 128.571...

I think for consistency, since the problem shows the triangle with exact 60°, and square will be 90°, pentagon 108°, hexagon 120°, octagon 135° — all whole numbers except heptagon.

But heptagon is unavoidable. So we’ll write it as approximately 128.6° or exact fraction?

Actually, let me check online or recall: regular heptagon interior angle is 900/7 degrees, which is about 128.57°.

In educational contexts, they often say “round to the nearest degree” or “leave as fraction”. But since the problem doesn’t specify, and other answers are integers, perhaps we should write the exact value as a mixed number or decimal?

Wait — let’s see the instruction: “Find the measure...” — probably expects numerical value.

I think safest is to write the exact decimal rounded to two places, or perhaps the problem expects us to use the formula and compute.

Alternatively, maybe I miscounted the shapes?

Looking back at the image description (even though I’m not supposed to describe it), there are six shapes: triangle, square, pentagon, hexagon, heptagon, octagon.

Heptagon has 7 sides — correct.

Perhaps in some curricula, they skip heptagon? No, it’s there.

Another thought: maybe the last one is not octagon? Let me count vertices.

From top left: triangle (3), square (4), then below: pentagon (5), hexagon (6), then bottom row: left is heptagon (7), right is octagon (8). Yes.

So for heptagon, we have to deal with non-integer.

But let’s proceed and write it as 128.57° or perhaps 128.6°? I think for accuracy, we’ll use two decimals.

Actually, let me calculate precisely:

900 ÷ 7 = 128.57142857...

So to two decimal places: 128.57°

But in many textbooks, they might write it as 128.6° if rounding to one decimal.

To be safe, I’ll use two decimals.

Now, let’s tabulate all:

| Polygon | Sides (n) | Sum of Interior Angles | Each Interior Angle |
|-------------|-----------|------------------------|---------------------|
| Triangle | 3 | 180° | 60° |
| Square | 4 | 360° | 90° |
| Pentagon | 5 | 540° | 108° |
| Hexagon | 6 | 720° | 120° |
| Heptagon | 7 | 900° | 128.57° |
| Octagon | 8 | 1080° | 135° |

Wait — is heptagon really 900°? Let me verify formula again.

Formula: (n-2)*180

For n=7: 5*180=900 — yes.

Each angle: 900/7 ≈ 128.571 — yes.

But I recall that sometimes people make mistakes here. Let me think differently.

Another way: exterior angle of regular polygon is 360/n, then interior = 180 - exterior.

For heptagon: exterior = 360/7 ≈ 51.4286°, so interior = 180 - 51.4286 = 128.5714° — same thing.

So correct.

Now, for the answer, since the problem says "find the measure", and for heptagon it's not integer, we'll present it as is.

But perhaps in the context of the worksheet, they expect students to compute using the formula and write the result.

Maybe I should write the exact fraction? Like 900/7 degrees? But that might not be expected.

Looking at the triangle example, they wrote 60° + 60° + 60° = 180°, so they showed addition.

For others, we can't easily add, so formula is fine.

I think for final answer, we'll list each polygon with its sum and each angle.

Now, to present clearly.

Final Answer should include all six polygons.

Let me write them in order as per image: top row left to right: triangle, square; middle row: pentagon, hexagon; bottom row: heptagon, octagon.

So:

- Triangle: each angle 60°, sum 180°
- Square: each angle 90°, sum 360°
- Pentagon: each angle 108°, sum 540°
- Hexagon: each angle 120°, sum 720°
- Heptagon: each angle ≈128.57°, sum 900°
- Octagon: each angle 135°, sum 1080°

But for heptagon, to be precise, perhaps write 128.57° or 128.6°? I think 128.57° is fine, but let's see if we can write it as a fraction.

900/7 = 128 4/7 degrees, but that might be messy.

Since the problem likely expects decimal, and to match precision, I'll use two decimals.

Actually, upon second thought, in many standardized tests, they avoid heptagon for this reason, but since it's here, we'll handle it.

Perhaps the last shape is not heptagon? Let me double-check the image description.

The user said: "Regular Polygons Worksheet" and listed shapes. From common worksheets, after hexagon is often heptagon then octagon.

But to confirm, a heptagon has 7 sides, octagon 8.

In the bottom row, left shape: let's imagine — if it's symmetric, heptagon has 7 sides, which is odd, so it might look a bit different, but in diagram, it's drawn with 7 sides.

I think it's correct.

So for final answer, I'll write:

For each polygon:

- Triangle: Each interior angle = 60°, Sum = 180°
- Square: Each interior angle = 90°, Sum = 360°
- Pentagon: Each interior angle = 108°, Sum = 540°
- Hexagon: Each interior angle = 120°, Sum = 720°
- Heptagon: Each interior angle = 128.57°, Sum = 900°
- Octagon: Each interior angle = 135°, Sum = 1080°

But to be accurate, let's calculate heptagon exactly: 900 ÷ 7 = 128.571428... so if we round to two decimal places, it's 128.57°.

Some might argue to round to nearest whole number, but 128.57 is closer to 129? No, 128.57 is less than 128.5? 128.57 is greater than 128.5, so to nearest whole number it would be 129°, but that's approximate.

I think for math problems, unless specified, we keep it as exact as possible. Since 900/7 is exact, but decimal is repeating, perhaps write as fraction.

But I recall that in such worksheets, they often have only polygons with integer interior angles, so maybe I misidentified.

Let me count the sides of the bottom-left shape.

In a typical "regular polygons worksheet", the sequence is triangle, square, pentagon, hexagon, heptagon, octagon — and heptagon is included.

Upon quick search in my mind, regular heptagon interior angle is indeed approximately 128.57 degrees.

So I'll go with that.

Perhaps the problem expects us to write the sum and then each angle, and for heptagon, write 900/7 or something, but I think for student level, decimal is fine.

Another idea: maybe the bottom-left is not heptagon but something else? Let's think — after hexagon (6), next could be heptagon (7), then octagon (8).

Yes.

So I'll proceed.

Final Answer:

Triangle: Each interior angle = 60°, Sum = 180°
Square: Each interior angle = 90°, Sum = 360°
Pentagon: Each interior angle = 108°, Sum = 540°
Hexagon: Each interior angle = 120°, Sum = 720°
Heptagon: Each interior angle = 128.57°, Sum = 900°
Octagon: Each interior angle = 135°, Sum = 1080°

But to make it neat, perhaps list in a box or something.

Since the instruction is to provide final answer after reasoning, and no specific format, I'll write it clearly.

Also, for heptagon, to be precise, let's use 128.57° (rounded to two decimal places).

Some sources say 128.6°, but I think two decimals is better.

Actually, let's calculate: 900 / 7 = 128.57142857, so to two decimals, it's 128.57 because the third digit is 1<5, so no rounding up.

128.571 — the digit after hundredths is 1, which is less than 5, so 128.57°.

Yes.

So final answer.