Chloe George If m_ABD = 83° and m_ABC = (x + 10) ° and mZDBC = (4x - 12), what is the measure of each angle?

ABC  = 27

DBC  = 56

Step-by-step explanation:

ABC + CBD = ABD

x+10 + 4x-12 = 83

Combine like terms

5x -2 = 83

Add 2 to each side

5x-2+2 = 83+2

5x = 85

Divide each side by 5

5x/5 = 85/5

x =17

ABC = x+10 = 17+10 = 27

DBC = 4x-12 = 4*17 -12 = 68-12 = 56

Angle ABC = 27°

Angle DBC = 56°

Step-by-step explanation:

So we have to set an equation first.

x + 10 + 4x - 12 = 83

This simplified = 5x - 2 = 83

--> 5x = 85

so x = 17

Plug it in to the formula for ABC and DBC

ABC = x + 10

17 + 10 = 27

ABC = 27

DBC = 4x - 12

68 - 12

DBC = 56

Thus, we have our 2 answers.

Hope this helps!

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