To find the measure of angle $\angle A$ in this triangle, we can use the fact that the sum of the interior angles in any triangle is always $180^\circ$.

Given:

• $\angle B = 75^\circ$
• $\angle C = 50^\circ$

We can set up the equation: $\angle A + \angle B + \angle C = 180^\circ$

Substituting the known values: $\angle A + 75^\circ + 50^\circ = 180^\circ$

Combining the angles: $\angle A + 125^\circ = 180^\circ$

Subtracting $125^\circ$ from both sides: $\angle A = 180^\circ - 125^\circ = 55^\circ$

So, the measure of $\angle A$ is: $\boxed{55^\circ}$

Would you like further explanation or have any questions?

Here are 5 related questions to deepen understanding:

1. What are the properties of the angles in an equilateral triangle?
2. How would you calculate an unknown angle in a quadrilateral?
3. How does the sum of interior angles change with the number of sides in a polygon?
4. How can you identify if a triangle is acute, obtuse, or right-angled based on its angle measures?
5. How does the exterior angle of a triangle relate to the opposite interior angles?

Tip: Remember, the sum of the interior angles of a triangle is always $180^\circ$, which is helpful for solving unknown angles.