To prove that if one angle of a triangle is 90 degrees, then the other two angles must add up to 90 degrees, we can use the properties of triangles.
We start with the basic fact that the sum of all interior angles in any triangle is always 180 degrees. This is a fundamental property of triangles.
Let’s denote the angles of the triangle as follows:
- Angle A = 90 degrees (the right angle)
- Angle B = ?
- Angle C = ?
According to the triangle angle sum property, we have:
Angle A + Angle B + Angle C = 180 degrees
Substituting the value of Angle A:
90 degrees + Angle B + Angle C = 180 degrees
Now, if we subtract 90 degrees from both sides of the equation, we get:
Angle B + Angle C = 180 degrees – 90 degrees
This simplifies to:
Angle B + Angle C = 90 degrees
This shows that the sum of the other two angles (Angle B and Angle C) in the triangle, when one angle is 90 degrees, is 90 degrees. Thus, we have proven that if one angle of a triangle is 90 degrees, then the other two angles must indeed add up to 90 degrees.