Answer key for angles in a triangle worksheet, displaying eight triangles with labeled angles and classifications.

To solve the problems involving the angles in triangles, we need to use the fundamental property of triangles: the sum of the interior angles of a triangle is always 180°. Let's go through each problem step by step.

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Problem 1:

The triangle has angles \(60^\circ\) and \(30^\circ\). We need to find the third angle.

- Sum of angles in a triangle: \(180^\circ\)
- Given angles: \(60^\circ\) and \(30^\circ\)
- Third angle = \(180^\circ - (60^\circ + 30^\circ) = 180^\circ - 90^\circ = 90^\circ\)

So, the third angle is \(\boxed{90^\circ}\).

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Problem 2:

The triangle has angles \(50^\circ\) and \(40^\circ\). We need to find the third angle.

- Sum of angles in a triangle: \(180^\circ\)
- Given angles: \(50^\circ\) and \(40^\circ\)
- Third angle = \(180^\circ - (50^\circ + 40^\circ) = 180^\circ - 90^\circ = 90^\circ\)

So, the third angle is \(\boxed{90^\circ}\).

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Problem 3:

The triangle has angles \(100^\circ\) and \(40^\circ\). We need to find the third angle.

- Sum of angles in a triangle: \(180^\circ\)
- Given angles: \(100^\circ\) and \(40^\circ\)
- Third angle = \(180^\circ - (100^\circ + 40^\circ) = 180^\circ - 140^\circ = 40^\circ\)

So, the third angle is \(\boxed{40^\circ}\).

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Problem 4:

The triangle has angles \(70^\circ\) and \(20^\circ\). We need to find the third angle.

- Sum of angles in a triangle: \(180^\circ\)
- Given angles: \(70^\circ\) and \(20^\circ\)
- Third angle = \(180^\circ - (70^\circ + 20^\circ) = 180^\circ - 90^\circ = 90^\circ\)

So, the third angle is \(\boxed{90^\circ}\).

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Problem 5:

The triangle is an isosceles triangle with angles \(75^\circ\) and \(30^\circ\). We need to find the third angle.

- Sum of angles in a triangle: \(180^\circ\)
- Given angles: \(75^\circ\) and \(30^\circ\)
- Third angle = \(180^\circ - (75^\circ + 30^\circ) = 180^\circ - 105^\circ = 75^\circ\)

So, the third angle is \(\boxed{75^\circ}\).

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Problem 6:

The triangle is an equilateral triangle with one angle given as \(60^\circ\). We need to find the other two angles.

- In an equilateral triangle, all three angles are equal.
- Each angle = \(60^\circ\)

So, the other two angles are \(\boxed{60^\circ}\) and \(\boxed{60^\circ}\).

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Problem 7:

The triangle has angles \(52^\circ\) and \(38^\circ\). We need to find the third angle.

- Sum of angles in a triangle: \(180^\circ\)
- Given angles: \(52^\circ\) and \(38^\circ\)
- Third angle = \(180^\circ - (52^\circ + 38^\circ) = 180^\circ - 90^\circ = 90^\circ\)

So, the third angle is \(\boxed{90^\circ}\).

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Problem 8:

The triangle is an isosceles right triangle with angles \(45^\circ\) and \(45^\circ\). We need to find the third angle.

- Sum of angles in a triangle: \(180^\circ\)
- Given angles: \(45^\circ\) and \(45^\circ\)
- Third angle = \(180^\circ - (45^\circ + 45^\circ) = 180^\circ - 90^\circ = 90^\circ\)

So, the third angle is \(\boxed{90^\circ}\).

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Final Answers:

1. \(\boxed{90^\circ}\)
2. \(\boxed{90^\circ}\)
3. \(\boxed{40^\circ}\)
4. \(\boxed{90^\circ}\)
5. \(\boxed{75^\circ}\)
6. \(\boxed{60^\circ}\) and \(\boxed{60^\circ}\)
7. \(\boxed{90^\circ}\)
8. \(\boxed{90^\circ}\)

Thus, the final answer is: \(\boxed{90^\circ, 90^\circ, 40^\circ, 90^\circ, 75^\circ, 60^\circ, 60^\circ, 90^\circ, 90^\circ}\).