A triangle has two angles measuring 40° and 65° . Use the Triangle Angle Sum Theorem to find the measure of the third angle.
The Triangle Angle Sum Theorem states that the sum of the three angles in a triangle is always 180°.
Let's denote the measure of the third angle as x.
Therefore, we have the equation:
40° + 65° + x = 180°
Combining like terms, we have:
105° + x = 180°
Next, we can isolate x by subtracting 105° from both sides:
x = 180° - 105°
x = 75°
Therefore, the measure of the third angle is 75°.