Question

using algebra $overrightarrow{bd}$ bisects $angle abc$. find the value of $x$. 44. $(x + 15)^{circ}$ $(4x - 45)^{circ}$

Explanation:

Step1: Set up equation

Since $\overrightarrow{BD}$ bisects $\angle ABC$, we have $\angle ABD=\angle DBC$. So, $x + 15=4x-45$.

Step2: Isolate x - terms

Subtract $x$ from both sides: $x+15 - x=4x - 45-x$, which simplifies to $15 = 3x-45$.

Step3: Isolate the constant - term

Add 45 to both sides: $15 + 45=3x-45 + 45$, resulting in $60 = 3x$.

Step4: Solve for x

Divide both sides by 3: $\frac{60}{3}=\frac{3x}{3}$, so $x = 20$.

Answer:

$x = 20$