Answer:
To calculate the interior angles of a triangle, we need to understand some basic principles of geometry.
1. Principle 1: The sum of the interior angles of a triangle is always 180°. This is a fundamental rule in Euclidean geometry, which is the study of flat space. It's based on the definition of a triangle as a three-sided polygon.
2. Principle 2: Each angle in a triangle is measured in degrees (°). Degrees are a unit of measurement for angles, just like meters or feet are units of measurement for distance. There are 360° in a full circle, so an angle that measures 180° is half of a full circle.
Now, let's apply these principles to calculate the third angle in a triangle with angles measuring 30° and 60°.
3. Step 1: Add the two known angles together. If one angle measures 30° and another measures 60°, their sum is 30° + 60° = 90°.
4. Step 2: Subtract the sum from 180° to find the third angle. Since the sum of all three angles must be 180°, we can find the third angle by subtracting the sum of the known angles from 180°. So, 180° - 90° = 90°.
Therefore, the third angle in a triangle with angles measuring 30° and 60° is 90°.