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3 years ago

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Mathematics

1 answer:

Alborosie3 years ago

4 0

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°

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