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Question
Two angles of a triangle measure 39.5° and 61.7°. Using the Triangle Angle Sum Theorem, which states that the sum of the inside angles of all triangles must equal 180°, find the measure of the third angle. (2 points)
Responses

68.8°
68.8°

78.8°
78.8°

88.8°
88.8°

98.8°

Answer 1

To find the measure of the third angle in the triangle, we can use the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in a triangle is equal to 180°.

We have two angles:
- Angle 1: 39.5°
- Angle 2: 61.7°

Now we can calculate the third angle (let's call it Angle 3) using the following formula:

\[
\text{Angle 3} = 180° - (\text{Angle 1} + \text{Angle 2})
\]

Substituting the known values:

\[
\text{Angle 3} = 180° - (39.5° + 61.7°)
\]

Calculating the sum of the two known angles:

\[
39.5° + 61.7° = 101.2°
\]

Now substitute this value back into the equation for Angle 3:

\[
\text{Angle 3} = 180° - 101.2° = 78.8°
\]

Therefore, the measure of the third angle is **78.8°**.