Question

study the example showing how to use angle relationships to solve problems. then solve problems 1 - 5. example what is the value of x? ∠acd and ∠hfg are same - side exterior angles. bd and eg are parallel, so m∠acd + m∠hfg = 180°. 3x + 6x + 81 = 180 9x = 99 x = 11 1 what is the angle relationship between ∠dcf and ∠cfg in the example? what are the measures of these angles? show your work. 2 find the value of x. show your work. (x - 50)° x°

Explanation:

Step1: Identify angle - relationship for problem 1

$\angle DCF$ and $\angle CFG$ are same - side interior angles. Since $\overleftrightarrow{BD}\parallel\overleftrightarrow{EG}$, same - side interior angles are supplementary, so $m\angle DCF + m\angle CFG=180^{\circ}$. First, we know from the example that $x = 11$. Then $m\angle DCF=3x=3\times11 = 33^{\circ}$ and $m\angle CFG=6x + 81=6\times11+81=66 + 81=147^{\circ}$.

Step2: Solve for $x$ in problem 2

The angles $(x - 50)^{\circ}$ and $x^{\circ}$ are same - side interior angles. Since the lines are parallel, they are supplementary. So we set up the equation $(x - 50)+x=180$. Combine like terms: $2x-50 = 180$. Add 50 to both sides: $2x=180 + 50=230$. Divide both sides by 2: $x = 115$.

Answer:

1. The angle - relationship between $\angle DCF$ and $\angle CFG$ is that they are same - side interior angles. $m\angle DCF = 33^{\circ}$ and $m\angle CFG=147^{\circ}$.
2. $x = 115$