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Chapter 2: Problem 74

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

Short Answer

Expert verified
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 by step solution

01

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.
02

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 \( A + B \).
03

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.

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