To solve this problem, let's start by defining some variables. Let's say that the measure of the original angle is x degrees.
Now, let's consider the complement of the original angle. The complement of an angle is the angle that, when added to the original angle, forms a 90-degree angle (a right angle). Therefore, the complement of the original angle is 90 - x degrees.
According to the problem, the bisector of the angle divides it into two angles, each of which has a measure of 15 degrees less than the complement of the angle. So, each of these angles can be expressed as (90 - x) - 15 = 75 - x degrees.
Since the bisector divides the original angle into two angles, their sum should be equal to the original angle. Therefore, we can write the equation:
(75 - x) + (75 - x) = x
Simplifying the equation, we have:
150 - 2x = x
Now, let's solve for x:
3x = 150
x = 50
Hence, the measure of the original angle is 50 degrees.