lettersandnumber
lettersandnumber lettersandnumber
  • 10-01-2020
  • Mathematics
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∠ABC is adjacent to ∠CBD. If the m∠ABC=4x+23, m∠CBD=6x+7, and m∠ABD=130°, what is the measure of angle ABC? (Show your work)

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sam4040
sam4040 sam4040
  • 18-01-2020

Answer:

[tex]\angle ABC=63\textdegree[/tex]

Step-by-step explanation:

[tex]\angle ABC=4x+23\\\angle CBD=6x+7\\\angle ABD=130\textdegree \\\angle ABD=\angle ABC+\angle CBD\\\\\Rightarrow4x+23+6x+7=130\\\Rightarrow10x+30=130\\\Rightarrow10x=100\\\Rightarrow x=10[/tex]

Substitute the value of [tex]x[/tex]

[tex]\angle ABC=4x+23\\=4\times10+23\\=40+23\\=63[/tex]

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