To determine the measure of the third angle in a triangle when two of its angles are given, you can use the following steps:
1. Understand the basic property of triangles: The sum of the interior angles of any triangle is always [tex]\(180^\circ\)[/tex].
2. Identify the given angles: In this problem, we are given two angles of the triangle, which are [tex]\(40^\circ\)[/tex] and [tex]\(60^\circ\)[/tex].
3. Set up the equation: To find the third angle, subtract the sum of the given angles from [tex]\(180^\circ\)[/tex]. In equation form:
[tex]\[
\text{Third angle} = 180^\circ - (\text{First angle} + \text{Second angle})
\][/tex]
4. Substitute the given values: Plug in the given angles:
[tex]\[
\text{Third angle} = 180^\circ - (40^\circ + 60^\circ)
\][/tex]
5. Perform the addition inside the parentheses:
[tex]\[
40^\circ + 60^\circ = 100^\circ
\][/tex]
6. Subtract to find the third angle:
[tex]\[
\text{Third angle} = 180^\circ - 100^\circ = 80^\circ
\][/tex]
So, the measure of the third angle in the triangle is [tex]\(80^\circ\)[/tex].
