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If the measures of two angles of a triangle are [tex]40^{\circ}[/tex] and [tex]60^{\circ}[/tex], find the third angle.

Sagot :

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].