The triangle angle sum theorem states that the sum of the interior angles of a triangle is always 180 degrees.
Given the two angles:
- Angle 1 = 25 degrees
- Angle 2 = 68 degrees
To find the third angle, we can set up the equation:
\[ \text{Third angle} = 180 - (\text{Angle 1} + \text{Angle 2}) \]
Substituting the values:
\[ \text{Third angle} = 180 - (25 + 68) \]
Calculating the sum of the angles first:
\[ 25 + 68 = 93 \]
Now, substituting back into the equation:
\[ \text{Third angle} = 180 - 93 = 87 \]
So, the third angle measures 87 degrees.
Thus, the correct answer is D: 87.