Question

what is measure of \\( \angle b \\) and \\( \angle e? \\)

\\( \angle b= \\)
\\( \angle e= \\)

Explanation:

Step1: Find the value of \( y \)

Since \( \angle A=\angle D \) (marked as equal in the figure) and \( \angle BFA=\angle ECD \) (vertically - opposite angles), by the Angle - Angle (AA) similarity criterion, \( \triangle ABF\sim\triangle DEC \). Then \( \angle B=\angle E \). So \( 3y = 6y-60 \).
Subtract \( 3y \) from both sides: \( 0=6y - 3y-60 \), which simplifies to \( 3y=60 \).
Divide both sides by 3: \( y = 20 \).

Step2: Calculate \( \angle B \) and \( \angle E \)

For \( \angle B \), substitute \( y = 20 \) into \( 3y \). So \( \angle B=3\times20=60^{\circ} \).
For \( \angle E \), substitute \( y = 20 \) into \( 6y - 60 \). So \( \angle E=6\times20-60=120 - 60=60^{\circ} \).

Answer:

\( \angle B = 60^{\circ} \), \( \angle E = 60^{\circ} \)