Final answer:
To find the measure of angle 3, we set up an equation using the fact that complementary angles add up to 90 degrees. We then solve for x and substitute it back into the expression for angle 3.
Step-by-step explanation:
In this problem, we are given that angle 3 and angle 9 are complementary. Complementary angles add up to 90 degrees. So, we can set up an equation: angle 3 + angle 9 = 90 degrees.
We are also given the measures of angle 3 and angle 9 as 3x - 7 and 4x - 1, respectively. Plugging these values into the equation, we get: (3x - 7) + (4x - 1) = 90 degrees.
Simplifying the equation, we have: 7x - 8 = 90 degrees. Solving for x, we find x = 13.
Now, we can substitute x back into the measure of angle 3 to find its value: angle 3 = 3x - 7 = 3(13) - 7 = 39 - 7 = 32 degrees.