Answer:
m∠GHE = 55°
Step-by-step explanation:
Angles in a quadrilateral sum to 360°. Therefore, for quadrilateral ABCD:
[tex]\sf m\angle B + m\angle BAD + m\angle CDA+ m\angle BCD = 360^{\circ}[/tex]
Given that m∠B = m∠BCD = 90° and m∠BAD = 125°, then:
[tex]\begin{aligned}\sf 90^{\circ} + 125^{\circ} + m\angle CDA + 90^{\circ} &= \sf 360^{\circ}\\\sf m\angle CDA + 305^{\circ} &= \sf 360^{\circ}\\\sf m\angle CDA + 305^{\circ} - 305^{\circ} &= \sf 360^{\circ} - 305^{\circ}\\\sf m\angle CDA &= \sf 55^{\circ}\end{aligned}[/tex]
As quadrilateral ABCD is congruent to quadrilateral EFGH, then:
[tex]\sf m\angle GHE = m\angle CDA = 55^{\circ}[/tex]
So, the measure of angle GHE is 55°.
