Question

in the paper airplane shown, (abcdcong efgh), (mangle b = mangle bcd=90), and (mangle bad = 131). find (mangle ghe).

Explanation:

Step1: Recall property of congruent polygons

Since \(ABCD\cong EFGH\), corresponding angles are equal. So \(\angle BAD=\angle FEH = 131^{\circ}\).

Step2: Consider angle - sum in a quadrilateral

In quadrilateral \(ABCD\), \(\angle B=\angle BCD = 90^{\circ}\), \(\angle BAD = 131^{\circ}\). Using the angle - sum property of a quadrilateral (\(\angle A+\angle B+\angle C+\angle D=360^{\circ}\)), we find \(\angle ADC=360-(90 + 90+131)=49^{\circ}\). And \(\angle EHG=\angle ADC = 49^{\circ}\) (corresponding angles of congruent polygons).

Step3: Analyze vertical angles

\(\angle DHE\) and \(\angle EHG\) are supplementary (linear - pair of angles). Let \(\angle DHE = x\), then \(x + \angle EHG=180^{\circ}\). So \(x = 180 - 49=131^{\circ}\).

Answer:

131