Answer:
In a triangle, the sum of the measures of the angles is always 180 degrees. So, we can set up an equation based on this fact and the given measures of angles 1 and 2:
m<1 + m<2 + m<3 = 180
Substituting the given measures, we get:
(5x+4) + (6x-6) + m<3 = 180
Simplifying and solving for m<3, we get:
m<3 = 180 - (5x+4) - (6x-6)
= 180 - 5x - 4 - 6x + 6
= 11x + 178
Therefore, the measure of angle 3 (m<3) in degrees is 11x + 178.