Question

1. find ( mangle d ).

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\).

Step2: Use the property of congruent sides in the quadrilateral

Since \(DG = GF\) and \(DE=EF\), \(\angle G=\angle F = 62^{\circ}\), \(\angle E = 146^{\circ}\)
Let \(m\angle D=x\). Then \(x+\angle G+\angle F+\angle E=360^{\circ}\)
Substitute the known values: \(x + 62^{\circ}+62^{\circ}+146^{\circ}=360^{\circ}\)

Step3: Solve for \(x\)

\(x+270^{\circ}=360^{\circ}\)
\(x=360^{\circ}- 270^{\circ}\)

Answer:

\(90^{\circ}\)