Find the missing angle α in various types of triangles including scalene, isosceles, and right triangles.

Explanation:
We need to find the missing angle α in each triangle. Remember:
The sum of all three angles in any triangle is always 180°.

Let’s go one by one:

1. Scalene Triangle: Angles given are 45° and 75°.
So, α = 180° − 45° − 75° = 60°.

2. Isosceles Triangle: One angle is 110°, and the other two are equal (since it’s isosceles, the base angles are equal). Let each base angle be α.
So: α + α + 110° = 180° → 2α = 70° → α = 35°.

3. Right Triangle: One angle is 90° (right angle), another is 60°, so:
α = 180° − 90° − 60° = 30°.

4. Scalene Triangle: Angles given are 70° and 30°.
α = 180° − 70° − 30° = 80°.

5. Isosceles Triangle: Two angles are equal — one is labeled α, and the other given is 40°. Since it’s isosceles and only one angle is shown as 40°, the two equal angles must be the ones marked α (the base angles), unless the 40° is the vertex angle. Looking at the diagram (standard layout), the 40° is at the bottom right, and the two top corners are marked α — but only one α is shown on the left side, and the right side has 40°, so likely the two equal angles are α and 40°? Wait — no, in an isosceles triangle, the two equal angles are opposite equal sides. In typical worksheet diagrams like this, if only one angle is labeled with a number and the other two are both labeled α, then those two α’s are equal. But here, triangle 5 shows: left angle = α, bottom right = 40°, and the top angle is unlabeled — but the triangle is labeled “Isosceles Triangle”, and only one α is drawn (on the left), and the right base angle is 40°. That suggests the two equal angles are α and 40°, meaning α = 40°, and the third angle is 180 − 40 − 40 = 100°. However, the problem says “Find the missing angle labelled α”, and only one angle is labeled α — so α is the unknown, and the other two are known or equal. Re-examining: In triangle 5, the diagram shows a triangle with one angle at the top labeled α, one at bottom right labeled 40°, and the left angle is not labeled — but since it's isosceles, and only one angle is given (40°), the most common case is that the two base angles are equal. If the 40° is a base angle, then the other base angle is also 40°, and α (top angle) = 180 − 40 − 40 = 100°. Yes — that matches standard presentation: in isosceles triangles on worksheets, when one base angle is given and the vertex is α, α is the top angle. So α = 100°.

6. Right Triangle: One angle is 90° (right angle), another is 65°, so:
α = 180° − 90° − 65° = 25°.

Let me double-check each:

1. 45 + 75 = 120 → 180 − 120 = 60 ✔
2. 110 + 35 + 35 = 180 ✔
3. 90 + 60 + 30 = 180 ✔
4. 70 + 30 = 100 → 180 − 100 = 80 ✔
5. Isosceles, two angles equal. Given one angle = 40°, and it's a base angle (typical), so other base = 40°, vertex α = 180 − 80 = 100 ✔
6. 90 + 65 = 155 → 180 − 155 = 25 ✔

All correct.

Final Answer:
1. 60°
2. 35°
3. 30°
4. 80°
5. 100°
6. 25°