Final answer:
To find the value of x and the measures of each angle in AMNP, we can use the properties of angles and solve the given equations. The value of x is 10, and the measures of the angles are: m/M = 37 degrees, m/N = 84 degrees, and m/P = 59 degrees.
Step-by-step explanation:
To find the value of x and the measures of each angle in AMNP, we need to apply the properties of angles and solve the given equations.
Given that m/M = (4x-3), m/N = (9x-6), and m/P = (6x-1), we can consider the following:
Angle MNP = m/M + m/N + m/P
Substitute the given expressions:
Angle MNP = (4x-3) + (9x-6) + (6x-1)
Combine like terms:
Angle MNP = 19x - 10
Since MNP is a triangle, the sum of its angles is 180 degrees:
19x - 10 = 180
Solve for x:
19x = 190
x = 10
Substitute x = 10 back into the expressions for m/M, m/N, and m/P to find their respective values:
m/M = (4x-3) = (4(10) - 3) = 37 degrees
m/N = (9x-6) = (9(10) - 6) = 84 degrees
m/P = (6x-1) = (6(10) - 1) = 59 degrees
Learn more about Angles in a Triangle