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 measures of the interior angles of a triangle is always 180 degrees.
Let's represent the measure of the third angle as x.
We know that the measures of the two given angles are 40 and 65 degrees.
Therefore, the sum of the measures of the three angles can be expressed as:
40 + 65 + x = 180 degrees
Simplifying this equation, we have:
105 + x = 180
Subtracting 105 from both sides, we get:
x = 180 - 105
x = 75
So, the measure of the third angle is 75 degrees.