Question

∠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)

Answer 1

`\angle ABC=63\textdegree`

Explanation:

`\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`

Substitute the value of
`x`

`\angle ABC=4x+23\\=4*10+23\\=40+23\\=63`