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Chapter 10: Problem 47

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 in a triangle can be found by subtracting the sum of the measures of the two known angles from 180 degrees, since the sum of all angles in a triangle is always 180 degrees.

Step by step solution

01

Understand the problem

Given a triangle with two known angles, the goal is to find the measure of the third angle. Here it is crucial to remember that the sum of all angles in a triangle is always \(180掳\).
02

Sum the known angles

Add the measures of the two known angles together. Let's denote the first angle as \(A\) and the second angle as \(B\), their sum will be \(A + B\).
03

Find the measure of the third angle

Subtract the sum of the two known angles from \(180掳\) to find the measure of the third unknown angle. Let's denote the third angle as \(C\), we can calculate it as \(C = 180掳 - (A + B)\). Here, \(C\) is the measurement of the third angle.

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