Question

1. solve for m∠cbd and m∠cbv setup: x= m\angle{cbd}= m\angle{cbv}=

Explanation:

Step1: Use angle - sum property

Since $\angle CBD+\angle CBV = 180^{\circ}$ (linear - pair of angles), we set up the equation $(9x - 2)+(20x + 5)=180$.
$(9x - 2)+(20x + 5)=180$ simplifies to $9x-2 + 20x+5=180$, then $29x+3 = 180$.

Step2: Solve for x

Subtract 3 from both sides of the equation $29x+3 = 180$:
$29x=180 - 3=177$.
Divide both sides by 29: $x=\frac{177}{29}=6$.

Step3: Find $m\angle CBD$

Substitute $x = 6$ into the expression for $\angle CBD$:
$m\angle CBD=9x - 2=9\times6-2=54 - 2=52^{\circ}$.

Step4: Find $m\angle CBV$

Substitute $x = 6$ into the expression for $\angle CBV$:
$m\angle CBV=20x + 5=20\times6+5=120 + 5=125^{\circ}$.

Answer:

setup: $(9x - 2)+(20x + 5)=180$
$x = 6$
$m\angle CBD=52^{\circ}$
$m\angle CBV=125^{\circ}$