The measure of the angle x on the diagram is 43 degrees
How to determine the measure of the angle x on the diagram
From the question, we have the following parameters that can be used in our computation:
Width = 12 cm
Both sides = 9 cm and 5 cm
The diagram that completes this question is added as an attachment
Using the law of cosines, we have the following equation
a² = b² + c² - 2bc * cos(A)
In this case,
A = x
So, we have
a² = b² + c² - 2bc * cos(x)
Substitute the known values into the equation
9² = 5² + 12² - 2 * 5 * 12 * cos(x)
This gives
81 = 169 - 120 * cos(x)
So, we have
cos(x) = [81 - 169]/[-120]
Evaluate
cos(x) = 0.7333
Take the arccos of both sides
x = 42.83 degrees
Approximate to the nearest degree
x = 43 degrees
Hence, the measure of the angle x is 43 degrees