Answer:
[tex]m\angle EFH=98\°[/tex]
Step-by-step explanation:
Given parallelogram EFGH for which
[tex]EF\parallel HG[/tex]
[tex]FG\parallel EH[/tex] [By definition of parallelogram]
Given [tex]m\angle FGH=82\°[/tex]
To find [tex]m\angle EFH[/tex]
We will apply angle properties of a parallelogram to get the required angle.
By property of parallelogram,
1) Opposite angles are congruent to each other
2) Adjacent angles are supplementary.
From the given parallelogram we know that [tex]m\angle FGH[tex] and [tex]m\angle EFH[/tex] are adjacent angles and thus they are supplementary angles by property of a parallelogram.
So, we can say.
[tex]m\angle FGH+m\angle EFH= 180\°[/tex] [By definition of supplementary angles]
Thus we have.
[tex]82\°+m\angle EFH= 180\°[/tex]
subtracting both sides by 82°
[tex]82\°+m\angle EFH-82\°= 180\°-82\°[/tex]
∴ [tex]m\angle EFH=98\°[/tex]
