To find the unknown angle $x$ in the triangle, we can use the fact that the sum of the angles in any triangle is always 180 degrees.

Given:

• One angle is $70^\circ$
• Another angle is not given directly, but we can find it since we know two sides and one angle

To solve for the angle $x$, follow these steps:

1. Use the Law of Sines to find the angle opposite the 10 cm side. $\frac{\sin(\text{angle opposite 14 cm})}{14} = \frac{\sin(70^\circ)}{10}$ Let's call the angle opposite the 14 cm side $A$. Therefore: $\sin(A) = \frac{14 \cdot \sin(70^\circ)}{10}$

2. Calculate $\sin(70^\circ)$: $\sin(70^\circ) \approx 0.9397$ So: $\sin(A) = \frac{14 \cdot 0.9397}{10} \approx 1.3156$

Since $\sin(A)$ cannot be greater than 1, there is an error in our calculation or our assumptions.

Re-evaluating, we recognize that perhaps we need the cosine rule instead.

1. Apply the Law of Cosines to find the angle opposite the 10 cm side: $c^2 = a^2 + b^2 - 2ab\cos(C)$ Where $c$ is 10 cm, $a$ is 14 cm, and $b$ is the side opposite to the given angle: $10^2 = 14^2 + x^2 - 2 \cdot 14 \cdot x \cdot \cos(70^\circ)$

Solving the triangle would typically involve solving the equation, but let's re-simplify it for a clearer angle:

To correctly solve:

• We first determine: $\cos(70^\circ) \approx 0.3420$

2. Insert: $10^2 = 14^2 + x^2 - 2 \cdot 14 \cdot x \cdot 0.3420$ Solving for all given angles.

However, without recalculating from basic provided sides, directly, if one angle is wrong, let's conclude our basic geometric solution here is incorrect without a correct intermediate re-assumed formula.

Does the correct derivation of side $x$ angles or steps provided hence result in correct answering through verification?

Alternatively, for clarity:

1. Understand the internal sum of angles.
2. Re-trace correct intermediate formula steps if direct sides given.

Would you like details or any further questions? Here are five related questions you may ask:

1. How do you find an angle in a triangle using the Law of Cosines?
2. Can you explain how to apply the Law of Sines to solve triangle problems?
3. What is the process for solving triangles with non-right angles?
4. How can trigonometric identities help in solving triangle problems?
5. What are common mistakes to avoid when solving for angles in triangles?

Tip: When solving triangle problems, always check if the angles and sides provided make sense with trigonometric rules and identities to avoid calculation errors.