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

1 answer

The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.

Let the three angles of the triangle be \( A \), \( B \), and \( C \). Given that:

  • \( A = 40^\circ \)
  • \( B = 65^\circ \)

We can find the third angle \( C \) using the theorem:

\[ C = 180^\circ - (A + B) \]

Now, substituting the known values:

\[ C = 180^\circ - (40^\circ + 65^\circ) \] \[ C = 180^\circ - 105^\circ \] \[ C = 75^\circ \]

Therefore, the measure of the third angle is \( 75^\circ \).