Answer:
60
Step-by-step explanation:
in order to find the measure of angle BOC we must first find x
If we look at the image we notice that angle AOC is made up of two angles; angle AOB and angle BOC
This means that angle AOC = angle AOB + angle BOC
If angle AOC = 104, angle AOB = 7x + 30 and angle BOC = 9x + 42 then 104 = 7x + 30 + 9x + 42
( note that we just created an equation that we can use to solve for x )
we now solve for x using the equation created
104 = 7x + 30 + 9x + 42
step 1 combine like terms
7x + 9x = 16x
30 + 42 = 72
we now have 104 = 16x + 72
step 2 subtract 72 from each side
104 - 72 = 32
72 - 72 cancels out
we now have 16x = 32
step 3 divide each side by 16
16x/16=x
32/16=2
we're left with x = 2
now that we have identified x let's find the measure of angle BOC
we can do this by simply substituting 2 for x in angle BOC's given expression ( 9x + 42 )
9x + 42
* substitute 2 for x *
9(2) + 42
simplify
9(2) = 18
18 + 42 = 60
angle BOC = 60
