Question

11 numeric 1 point line de is parallel to line fg. what is the measure of m∠fba (m∠v)? answer

Explanation:

Step1: Use linear - pair property

The angle adjacent to the $108^{\circ}$ angle and $\angle FBA$ (i.e., $\angle V$) forms a linear - pair. Let $\angle FBA=\angle V$ and the adjacent angle to the $108^{\circ}$ angle be $\angle U$. We know that the sum of angles in a linear - pair is $180^{\circ}$. So, $\angle U + 108^{\circ}=180^{\circ}$. Then $\angle U=180^{\circ}-108^{\circ}=72^{\circ}$.

Step2: Use the property of parallel lines and transversals

Since $DE\parallel FG$, and $AC$ is a transversal. The angle at $A$ ($30^{\circ}$) and the corresponding angle formed with respect to the parallel lines and transversal has no direct relation to finding $\angle V$ in this case. But we already found $\angle V$ from the linear - pair property.

Answer:

$72^{\circ}$