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In the given diagram, we are asked to find the value of angle \( A \) when angles \( B = 56^\circ \) and \( C = 75^\circ \).

This appears to be a problem involving angles in a triangle, where \( A^\circ \), \( B^\circ \), and \( C^\circ \) represent the interior angles of a triangle. The key geometric principle to use here is that the sum of the interior angles in any triangle is always \( 180^\circ \).

That is:
\[
A + B + C = 180^\circ
\]

Given:
\[
B = 56^\circ, \quad C = 75^\circ
\]

Substitute these values into the equation:
\[
A + 56^\circ + 75^\circ = 180^\circ
\]
\[
A + 131^\circ = 180^\circ
\]

Now, solve for \( A \):
\[
A = 180^\circ - 131^\circ = 49^\circ
\]

Thus, the value of \( A \) is \( 49^\circ \).

Would you like further details, or do you have any questions?

Here are 5 related questions to extend this problem:
1. What happens to the sum of the angles if the triangle is non-Euclidean (on a curved surface)?
2. How would you calculate the exterior angle at \( A \)?
3. Can you prove that the sum of the interior angles of a triangle is always 180 degrees?
4. What if the angle \( C \) were changed to \( 85^\circ \)? How would that affect angle \( A \)?
5. How would you solve for \( A \) if you were only given the exterior angles of the triangle?

**Tip:** When solving triangle problems, always check whether it's necessary to apply trigonometric rules or simply use the angle sum property.

Find the value of A if B = 56° and C = 75°.

Learn how to find the missing angle A in a triangle where angles B = 56° and C = 75°. Using the angle sum property, we show step-by-step how to calculate the missing angle. Suitable for students in Grades 7-9.

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