Option B: [tex]m \angle F=m \angle G=120^{\circ}[/tex] and [tex]m \angle E=60^{\circ}[/tex], so [tex]\angle E[/tex] is supplementary to both [tex]\angle F[/tex] and [tex]\angle G[/tex], so EFGH is a parallelogram.
Option C: [tex]m \angle F=m \angle G=120^{\circ}[/tex] so EFGH is a parallelogram.
Option D: [tex]m \angle E+m \angle G=180^{\circ}[/tex] so EFGH is a parallelogram.
Explanation:
Option A: [tex]m \angle E=m \angle F=60^{\circ}[/tex] and [tex]m \angle G=120^{\circ}[/tex] so [tex]\angle G[/tex] is supplementary to both [tex]\angle E[/tex] and [tex]\angle F[/tex], so EFGH is a parallelogram
Let us substitute [tex]y=7[/tex] and [tex]z=9[/tex] in [tex]m \angle E=(7y+11)^{\circ}[/tex], [tex]m \angle F=(17y+1)^{\circ}[/tex] and [tex]m \angle G=(14z-6)^{\circ}[/tex] to determine the exact measures the angles of the parallelogram.
Substituting, we get, [tex]m \angle E=60^{\circ}[/tex], [tex]m \angle F=m \angle G=120^{\circ}[/tex]
Thus, [tex]m \angle E\neq m \angle F[/tex] because the measures of these angles are not equal.
Hence, Option A is not the correct answer.
Option B: [tex]m \angle F=m \angle G=120^{\circ}[/tex] and [tex]m \angle E=60^{\circ}[/tex], so [tex]\angle E[/tex] is supplementary to both [tex]\angle F[/tex] and [tex]\angle G[/tex], so EFGH is a parallelogram.
Let us substitute [tex]y=7[/tex] and [tex]z=9[/tex] in [tex]m \angle E=(7y+11)^{\circ}[/tex], [tex]m \angle F=(17y+1)^{\circ}[/tex] and [tex]m \angle G=(14z-6)^{\circ}[/tex] to determine the exact measures the angles of the parallelogram.
Thus, substituting, we have, [tex]m \angle E=60^{\circ}[/tex], [tex]m \angle F=m \angle G=120^{\circ}[/tex]
Hence, Option B is the correct answer.
Option C: [tex]m \angle F=m \angle G=120^{\circ}[/tex] so EFGH is a parallelogram.
To determine the angles, let us substitute [tex]z=9[/tex] in [tex]m \angle F=(17y+1)^{\circ}[/tex] and [tex]m \angle G=(14z-6)^{\circ}[/tex]
Thus, [tex]m \angle F=m \angle G=120^{\circ}[/tex]
Since, the opposite angles of a parallelogram are equal, EFGH is a parallelogram.
Hence, Option C is the correct answer.
Option D: [tex]m \angle E+m \angle G=180^{\circ}[/tex] so EFGH is a parallelogram.
Let us substitute [tex]y=7[/tex] and [tex]z=9[/tex] in [tex]m \angle E=(7y+11)^{\circ}[/tex], [tex]m \angle F=(17y+1)^{\circ}[/tex] and [tex]m \angle G=(14z-6)^{\circ}[/tex] to determine the exact measures the angles of the parallelogram.
Substituting, we have, [tex]m \angle E=60^{\circ}[/tex], [tex]m \angle F=m \angle G=120^{\circ}[/tex]
Adding the angles E and G, we have,
[tex]m \angle E+m \angle G=60^{\circ}+120^{\circ}=180^{\circ}[/tex]
By the property of parallelogram, any two adjacent angles add upto 180.
Thus, the adjacent angles E and G add upto 180.
Hence, Option D is the correct answer.
