Worksheet #2 on angle measures in polygons, featuring six problems involving triangle and polygon angle calculations.

Let’s solve each problem one by one, step by step.

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Problem 1:

In a triangle, the sum of all three angles is always 180°.

We are told:
- One angle = 46°
- Another angle = 108°

Add them:
46 + 108 = 154°

Subtract from 180 to find the missing angle:
180 - 154 = 26°

✔ So, the remaining angle is 26°.

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Problem 2:

In a quadrilateral (4-sided shape), the sum of all interior angles is 360°.

We are told:
- Two angles are 37° each → 37 + 37 = 74°
- One angle is 118°

Add those together:
74 + 118 = 192°

Subtract from 360:
360 - 192 = 168°

✔ So, the remaining angle is 168°.

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Problem 3:

The formula for the sum of interior angles of a polygon with *n* sides is:

> (n - 2) × 180°

We’re told the sum is 540°, so set up the equation:

(n - 2) × 180 = 540

Divide both sides by 180:

n - 2 = 3

Add 2 to both sides:

n = 5

A polygon with 5 sides is called a pentagon.

✔ So, it’s a pentagon.

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Problem 4:

A hexagon has 6 sides, so the sum of its interior angles is:

(6 - 2) × 180 = 4 × 180 = 720°

We’re told that five of the angles are 110° each.

So, 5 × 110 = 550°

Subtract from total to find the last angle:

720 - 550 = 170°

✔ So, the remaining angle is 170°.

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Problem 5:

Again, use the formula: (n - 2) × 180 = sum of interior angles

Given sum = 1440°

Set up:

(n - 2) × 180 = 1440

Divide both sides by 180:

n - 2 = 8

Add 2:

n = 10

A 10-sided polygon is called a decagon.

✔ So, it’s a decagon.

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Problem 6:

Check if the three angles add up to 180° (required for any triangle).

1° + 2° + 177° = 180°

Yes! They add up exactly to 180°.

Even though two angles are very small and one is almost flat, mathematically, this still forms a valid triangle — just a very “skinny” one.

✔ So, yes, it is possible.

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Final Answer:
1) 26°
2) 168°
3) Pentagon
4) 170°
5) Decagon
6) Yes