Answer:
CBA = 53°
DBC = 39°
Step-by-step explanation:
You have 2 angles, CBA and DBC.
Together, these form the angle DBA. (See attached image)
We know the following about the 2 angles:
CBA = 8x - 3
DBC = 5x + 4
Like we said, both of these together form the angle DBA. Thus:
DBA = CBA + DBC
Let's put in the values we know, 8x-3, 5x+4, instead of CBA and DBC:
DBA = 8x - 3 + 5x + 4
DBA = 13x - 3 + 4
DBA = 13x + 1
We also know that:
DBA = 92 (from the question)
Let's set our expression 13x + 1 equal to 92.
DBA = 13x + 1
DBA = 92
13x + 1 = 92
Subtract 1 from both sides:
13x = 91
Divide both sides by 13:
x = 91 / 13
x = 7
Now that we know x, we can find what CBA and DBC are.
CBA = 8x - 3
Replace x with 7:
CBA = 8*7 - 3
CBA = 56 - 3
CBA = 53
DBC = 5x + 4
Replace x with 7:
DBC = 5*7 + 4
DBC = 35 + 4
DBC = 39
Answer:
CBA = 53°
DBC = 39°
