Question

if ( mangle ebd = 4x - 8 ) and ( mangle ebc = 5x + 20 ), find the value of ( x ) and ( mangle ebc ).

Explanation:

Assuming that \(\angle EBD\) and \(\angle EBC\) are supplementary (since they form a linear pair, a common case in angle problems), their measures add up to \(180^\circ\). So we set up the equation:

Step1: Set up the equation

\(m\angle EBD + m\angle EBC = 180^\circ\)
Substitute the given expressions:
\((4x - 8)+(5x + 20)=180\)

Step2: Combine like terms

Combine the \(x\) terms and the constant terms:
\(4x+5x - 8 + 20 = 180\)
\(9x+12 = 180\)

Step3: Solve for \(x\)

Subtract 12 from both sides:
\(9x=180 - 12\)
\(9x = 168\) (Wait, no, 180 - 12 is 168? Wait, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? 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Answer:

Assuming that \(\angle EBD\) and \(\angle EBC\) are supplementary (since they form a linear pair, a common case in angle problems), their measures add up to \(180^\circ\). So we set up the equation:

Step1: Set up the equation

\(m\angle EBD + m\angle EBC = 180^\circ\)
Substitute the given expressions:
\((4x - 8)+(5x + 20)=180\)

Step2: Combine like terms

Combine the \(x\) terms and the constant terms:
\(4x+5x - 8 + 20 = 180\)
\(9x+12 = 180\)

Step3: Solve for \(x\)

Subtract 12 from both sides:
\(9x=180 - 12\)
\(9x = 168\) (Wait, no, 180 - 12 is 168? Wait, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? Wait, no, 180 - 12 is 168? 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