If a triangle has angles measuring 35 degrees and 75 degrees, what is the measure of the third angle?

To determine the measure of the third angle in a triangle when the measures of the other two angles are given, you can use the fundamental property of triangles: the sum of the interior angles in any triangle is always 180 degrees.

In this case, the two known angles measure 35 degrees and 75 degrees. To find the third angle, you add these two angles together:

35 degrees + 75 degrees = 110 degrees.

Next, subtract this sum from 180 degrees to find the measure of the third angle:

180 degrees - 110 degrees = 70 degrees.

Thus, the measure of the third angle is 70 degrees, confirming that this answer is logically consistent with the properties of triangles.