Questions: Angle ABC is bisected by BD→. For what value of x will DX=DY be true?

Transcript text: $\angle A B C$ is bisected by $\overrightarrow{B D}$. For what value of x will $\overline{D X}=\overline{D Y}$ be true?

Solution

Step 1: Understand the Problem

The problem states that $\angle ABC$ is bisected by $\overline{BD}$. We need to find the value of $x$ for which $DX = DY$.

Step 2: Set Up the Equation

Since $\angle ABC$ is bisected by $\overline{BD}$, the lengths $DX$ and $DY$ must be equal. Given: \[ DX = 5x + 4 \] \[ DY = 19 \]

Step 3: Equate the Expressions

Since $DX = DY$, we can set the expressions equal to each other: \[ 5x + 4 = 19 \]

Step 4: Solve for $x$

Subtract 4 from both sides: \[ 5x = 15 \] Divide both sides by 5: \[ x = 3 \]

The value of $x$ for which $DX = DY$ is $x = 3$.

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