The measure of the smallest angle C is 85.
To find the measure of angle C, you need to set up an equation based on the fact that the sum of angles in a triangle is 180 degrees.
The given angles are:
C=(15x+25)
A=(7x+22)
B=(10x+5)
The sum of angles in a triangle is 180 , so:
C+A+B=180
Substitute the expressions for angles C, A, and B:
(15x+25)+(7x+22)+(10x+5)=180
Combine like terms:
32x+52=180
Now, solve for x:
32x=128
x=4
Now that you have the value of x, you can find the measure of the smallest angle C by plugging in x=4 into the expression for C:
C=(15x+25)
C=(15(4)+25)
C=60+25
C=85
So, the measure of the smallest angle C is 85.