Question

ae = ec and bf = fc. ef = 10 and m∠efc = 92°. m∠dbf = ?°

Explanation:

Step1: Identify mid - points

Since $AE = EC$ and $BF=FC$, $E$ is the mid - point of $AC$ and $F$ is the mid - point of $BC$.

Step2: Consider the property of mid - points

In a triangle, the line segment joining the mid - points of two sides is parallel to the third side. So, $EF\parallel AB$.

Step3: Use the property of parallel lines and angles

Since $EF\parallel AB$, $\angle EFC$ and $\angle ABC$ are corresponding angles. So, $\angle ABC=\angle EFC = 92^{\circ}$. And $\angle DBF$ and $\angle ABC$ are the same angle.

Answer:

$92$