The answer is 66.4
==================================================
Explanation:
We have a right triangle because the square marker (angle C) indicates a right 90 degree angle. Therefore we can use a trig function to help find the measure of angle B.
With angle B as the reference angle, we see that segment BC = 4 is the adjacent side and segment AB = 10 is the hypotenuse. The ratio of the adjacent and hypotenuse is equal to the cosine of the reference angle
cos(angle) = adjacent/hypotenuse
cos(B) = BC/AB
cos(B) = 4/10
cos(B) = 0.4
Now use the inverse cosine or arccosine function to undo the cosine function on the left side. This will isolate B
cos(B) = 0.4
arccos(cos(B)) = arccos(0.4)
B = arccos(0.4)
B = 66.4218215217981 see note below
B = 66.4
-----
note: you will need your calculator for this step. Make sure your calculator is in degree mode. On many calculators, the inverse cosine button is marked as "cos" with a "-1" as an exponent. The result shown is approximate.
