Question

Two angles of a triangle measure 39.5°
and 61.7°
. Use the Triangle Angle Sum Theorem to find the measure of the third angle; do not round the answer.(1 point)
Responses

79°
79 degrees

78°
78 degrees

68.8°
68.8 degrees

78.8°

Answer 1

To find the measure of the third angle in a triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.

Let the third angle be \( x \). The two given angles are 39.5° and 61.7°. Thus, we have:

\[
39.5° + 61.7° + x = 180°
\]

First, calculate the sum of the two given angles:

\[
39.5° + 61.7° = 101.2°
\]

Now, substitute this sum into the equation:

\[
101.2° + x = 180°
\]

To find \( x \), subtract 101.2° from 180°:

\[
x = 180° - 101.2° = 78.8°
\]

Thus, the measure of the third angle is \( 78.8° \).

The correct response is:

**78.8°**