https://file.aiquickdraw.com/mathbot/file/1728201752614djsyktka.jpg

Let's analyze and solve each triangle step by step.

### 1. First Triangle (OQP):
- Given:
  - Angle \( \angle OQP = 48^\circ \)
  - Angle \( \angle OPQ = 57^\circ \)
  - Side \( OQ = 40 \, \text{cm} \)
- Unknown: \( \angle QOP \)

By the triangle angle sum property:
\[
\angle QOP = 180^\circ - 48^\circ - 57^\circ = 75^\circ
\]

You can now use the **Law of Sines** to find the missing sides if needed:
\[
\frac{OQ}{\sin(\angle OPQ)} = \frac{PQ}{\sin(\angle QOP)} = \frac{OP}{\sin(\angle OQP)}
\]

### 2. Second Triangle (ABC):
- Given:
  - \( \angle B = 70^\circ \)
  - \( \angle A = 80^\circ \)
  - \( AB = 7 \, \text{m} \)
- Unknown: \( \angle C \)

By the angle sum property:
\[
\angle C = 180^\circ - 70^\circ - 80^\circ = 30^\circ
\]

You can then apply the Law of Sines:
\[
\frac{AB}{\sin(\angle C)} = \frac{BC}{\sin(\angle A)} = \frac{AC}{\sin(\angle B)}
\]
to find the missing sides.

### 3. Third Triangle (RPS):
- Given:
  - \( \angle RSP = 96^\circ \)
  - \( \angle SRP = 12 \, \text{cm} \)
- Unknown: \( \angle PRS \)

Using the angle sum property:
\[
\angle PRS = 180^\circ - 96^\circ - 12^\circ = 72^\circ
\]

### 4. Fourth Triangle (QRS):
- Given:
  - \( \angle R = 118^\circ \)
  - Side \( RQ = 11 \)
- Unknown: \( \angle QRS \)

First, find \( \angle QRS \):
\[
\angle QRS = 180^\circ - 118^\circ = 62^\circ
\]

### 5. Fifth Triangle (ABC):
- Given:
  - \( \angle B = 47^\circ \)
  - \( \angle C = 8 \)
  - \( AC = 7 \)
  
By the angle sum property:
\[
\angle A = 180^\circ - 47^\circ - 8^\circ = 125^\circ
\]

Use the Law of Sines to find missing sides.

### 6. Sixth Triangle (ACD):
- Given:
  - \( \angle A = 106.4^\circ \)
  - Side \( AC = 7 \, \text{m} \)
- Unknown: Other angles

Using the angle sum:
\[
\angle C = 180^\circ - 106.4^\circ = 73.6^\circ
\]

Use Law of Sines for unknown sides.

### 7. Seventh Triangle (KLM):
- Given:
  - Side \( LM = 12 \)
  - \( MK = 13.2 \)

This appears to be a right triangle (no angles provided), so use the **Pythagorean theorem** to find side \( KL \):
\[
KL = \sqrt{MK^2 - LM^2}
\]

Let me know if you'd like more details on solving the sides, or if you have further questions.

---
### Related Questions:
1. How can we use the Law of Sines to find unknown sides in non-right triangles?
2. Can we apply the Law of Cosines in any of these cases, and how?
3. What is the importance of the angle sum property in solving triangle problems?
4. How can we check if a triangle is right-angled using its given sides?
5. What happens if one angle of a triangle is more than \(90^\circ\)?

### Tip:
Always begin by checking if the sum of angles matches \(180^\circ\) to confirm your triangle data is consistent before solving!

Find the unknowns in the triangles from the image.

This problem involves solving seven triangles using the triangle angle sum property, the Law of Sines, and the Pythagorean theorem. Suitable for students in Grades 9-12.

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