In a triangle, the sum of all angles is always $180^\circ$. Given that:

$\angle A = \angle B + \angle C$

we can substitute this into the equation for the sum of angles in a triangle:

$\angle A + \angle B + \angle C = 180^\circ$

Replacing $\angle A$ with $\angle B + \angle C$:

$(\angle B + \angle C) + \angle B + \angle C = 180^\circ$

Simplifying, we get:

$2(\angle B + \angle C) = 180^\circ$

Dividing by 2:

$\angle B + \angle C = 90^\circ$

Thus, $\angle A = 90^\circ$.

Would you like further clarification on the steps or have any questions?

Related Questions

1. How do you find the measure of angles in different types of triangles?
2. What are the properties of a right triangle?
3. How does the angle sum property of a triangle help in solving for unknown angles?
4. Can the sum of two angles ever exceed $180^\circ$ in a triangle?
5. What other triangle properties apply when one angle equals $90^\circ$?

Tip

In any triangle, if you know that one angle equals the sum of the other two, it's a right triangle, with the known angle as $90^\circ$.