Problem 74 - Introductory and Intermediate Algebra for College Students 4th

Question

If the measures of two angles of a triangle are known, explain how to find the measure of the third angle.

Step-by-Step Solution

Answer

The measure of the third angle of a triangle can be found by subtracting the sum of the measures of the first two angles from 180 degrees.

Step 1: Understand the Properties of a Triangle

The first step is to remember that the sum of the angles in a triangle always equals 180 degrees. This is a fundamental rule in geometry and is important to solve the problem.

Step 2: Add the Measures of the Known Angles

Next, add the measures of the two known angles. Let's denote the known angles as \( A \) and \( B \). So, the sum will be \( A + B \).

Step 3: Subtract to Find the Unknown Angle

To find the measure of the third angle which we'll denote as \( C \), subtract the sum of the known angle measures from 180. Mathematically, this step can be represented as: \( C = 180 - (A + B) \). This calculation gives us the measure of the third angle in the triangle.