Question

in the paper airplane shown, ( abcdcong efgh ), ( mangle b=mangle bcd = 90 ), and ( mangle bad = 125 ). find ( mangle ghe ).

Explanation:

Step1: Use the property of quadrilaterals

The sum of interior angles of a quadrilateral is \(360^{\circ}\). For quadrilateral \(ABCD\), we know \(m\angle B = 90^{\circ}\), \(m\angle BCD=90^{\circ}\), \(m\angle BAD = 125^{\circ}\). Let \(m\angle ADC=x\). Then \(90 + 90+125+x=360\).

Step2: Solve for \(m\angle ADC\)

Simplify the equation \(90 + 90+125+x=360\) to \(305+x = 360\). Subtract \(305\) from both sides: \(x=m\angle ADC=360 - 305=55^{\circ}\).

Step3: Use the property of congruent quadrilaterals

Since \(ABCD\cong EFGH\), corresponding angles are equal. \(\angle GHE\) and \(\angle ADC\) are corresponding angles.

Answer:

55