Finding unkown angles
We know m∠NBR can be written in two ways:
m∠NBR = 17x + 8 [given]
and
m∠NBR = (12x + 4) + 42 [observed in the drawing]
Then
17x + 8 = (12x + 4) + 42
17x + 8 = 12x + 46
Using this formula we can find x- value
Step 1
Rearranging the terms so the terms with the unkown variable x are on the left side and the other ones on the right side:
17x + 8 = 12x + 46
↓ substracting 12x both sides
-12x + 17x + 8 = 46
↓ substracting 8 both sides
-12x + 17x = - 8 + 46
5x = 38
Step 2
Solving the equation for x:
5x = 38
↓ dividing by 5 both sides
5x/5 = 38/5
x = 7.6
Answer 1: x = 7.6
Now we want to find m∠NBS
It is given that
m∠NBS = 12x + 4
to find it we just replace x by 7.6:
m∠NBS = 12 · 7.6 + 4
m∠NBS = 91.2 + 4
m∠NBS = 95.2
Answer 2: m∠NBS = 95.2