The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.
Given the measures of two angles in the triangle:
- Angle a = 120 degrees
- Angle b = 34 degrees
To find the measure of the third angle (let's call it angle c), we can use the following equation:
\[ \text{Angle a} + \text{Angle b} + \text{Angle c} = 180^\circ \]
Substituting the known values:
\[ 120^\circ + 34^\circ + \text{Angle c} = 180^\circ \]
Now, add the measures of angle a and angle b:
\[ 120^\circ + 34^\circ = 154^\circ \]
Now, we have:
\[ 154^\circ + \text{Angle c} = 180^\circ \]
To find angle c, subtract 154 degrees from both sides:
\[ \text{Angle c} = 180^\circ - 154^\circ = 26^\circ \]
Therefore, the measure of the third angle (angle c) is 26 degrees.