Question

1. $overline{bd}$ bisects $angle abc$. solve for $x$. 35° $(5x + 5)°$

Explanation:

Step1: Recall angle - bisector property

An angle - bisector divides an angle into two equal angles. So, if $\overline{BD}$ bisects $\angle ABC$, then $\angle ABD=\angle DBC$.

Step2: Set up the equation

We know that $\angle ABD = 35^{\circ}$ and $\angle DBC=(5x + 5)^{\circ}$. Set up the equation $35=5x + 5$.

Step3: Solve the equation for $x$

First, subtract 5 from both sides of the equation: $35−5=5x+5 - 5$, which simplifies to $30 = 5x$. Then divide both sides by 5: $\frac{30}{5}=\frac{5x}{5}$, so $x = 6$.

Answer:

$x = 6$