A triangle has two angles measuring 40° and 65° . Use the Triangle Angle Sum Theorem to find the measure of the third angle.

Answer 1

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°.