Question

look at this diagram: if (overleftrightarrow{bd}) and (overleftrightarrow{eg}) are parallel lines and (mangle dcf = 60^{circ}), what is (mangle dca?)

Explanation:

Step1: Recall angle - relationship

$\angle DCF$ and $\angle DCA$ are supplementary angles.

Step2: Use the supplementary - angle formula

Supplementary angles add up to 180°. Let $m\angle DCA=x$. Then $x + m\angle DCF=180^{\circ}$.

Step3: Substitute the value of $\angle DCF$

Given $m\angle DCF = 60^{\circ}$, we have $x+60^{\circ}=180^{\circ}$. Solving for $x$, we get $x=180^{\circ}-60^{\circ}$.

Answer:

$120$