Question

look at this diagram: if $overleftrightarrow{bd}$ and $overleftrightarrow{eg}$ are parallel lines and $mangle efh = 70^{circ}$, what is $mangle dca?$

Explanation:

Step1: Identify angle - relationship

$\angle EFH$ and $\angle FCD$ are corresponding angles. Since $\overleftrightarrow{BD}$ and $\overleftrightarrow{EG}$ are parallel lines, corresponding angles are congruent. So $m\angle FCD=m\angle EFH = 70^{\circ}$.

Step2: Note linear - pair relationship

$\angle FCD$ and $\angle DCA$ form a linear - pair. The sum of the measures of angles in a linear - pair is $180^{\circ}$. So $m\angle FCD + m\angle DCA=180^{\circ}$.

Step3: Solve for $m\angle DCA$

Substitute $m\angle FCD = 70^{\circ}$ into the equation $m\angle FCD + m\angle DCA=180^{\circ}$. We get $70^{\circ}+m\angle DCA = 180^{\circ}$. Then $m\angle DCA=180^{\circ}-70^{\circ}=110^{\circ}$.

Answer:

$110$