if the angles of a triangle with measures in the ratio of 5:6:7, then find the measure of the smallest angle.
a. 40 degrees
b. 50 degrees
c. 60 degrees
d. 70 degrees
The angles of a triangle always add up to 180 degrees.
Let's represent the measures of the angles as 5x, 6x, and 7x.
We know that 5x + 6x + 7x = 180.
Combining like terms, we have 18x = 180.
Divide both sides by 18, and we get x = 10.
Therefore, the measures of the angles are 5(10) = 50, 6(10) = 60, and 7(10) = 70.
The smallest angle is 50 degrees.
Therefore, the answer is b. 50 degrees.