The Angle ABM is 44 degrees and Angle MBC is 76 degrees.
To find the measure of each angle in terms of x, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's set up an equation:
Angle ABC + Angle ABM + Angle MBC = 180
90 + 2x + 20 + 3x + 40 = 180
5x + 150 = 180
Now, we can solve for x:
5x = 60
x = 12
Now we can substitute the value of x back into the expressions for the angles to find their measures:
Angle ABM = 2*12 + 20 = 2(12) + 20 = 44 degrees
Angle MBC = 3*12 + 40 = 3(12) + 40 = 76 degrees
The probable question may be:
Use an algebraic equation to find the measure of each angle that is represented in terms of x.
In triangle ABC , BM is angle bisector, Angle ABC= 90 degree, Angle ABM=2x+20 degree, angle MBC=3x+40 degree
measure of angle 2x+20 degree=_____degree
measure of angle 3x+40 degree=_____degree