The image shows a triangle where two angles are labeled: 50° and 70°. The third angle is expressed as $2u$, and we are tasked with finding the value of $u$.

Solution using the Triangle Angle Sum Theorem:

The sum of the interior angles in any triangle is always 180°. Therefore, we can write the equation:

$50^\circ + 70^\circ + 2u = 180^\circ$

Now, solve for $u$:

1. Add the known angles: $50^\circ + 70^\circ = 120^\circ$

2. Subtract from 180° to find $2u$: $2u = 180^\circ - 120^\circ = 60^\circ$

3. Solve for $u$ by dividing by 2: $u = \frac{60^\circ}{2} = 30^\circ$

Thus, the value of $u$ is 30°.

Would you like more details or have any questions?

Here are five related questions to further explore:

1. What happens to the angles in an isosceles triangle?
2. How do we apply the exterior angle theorem to this triangle?
3. Can you use the same approach to find the angles of a right triangle?
4. What is the relationship between the angles in an equilateral triangle?
5. How do supplementary and complementary angles relate to triangle angle sums?

Tip: Always remember that the sum of the angles in any triangle is 180°, which is crucial for solving problems like this.