Question

In parallelogram DEFG D=(5x-8) and E=(3x+28). How many degrees is F

Answer 1

The angle of F in degrees is 92°

Adjacent angles of a parallelogram are supplementary.

Therefore,

Therefore,

5x - 8 + 3x + 28 = 180

8x + 20 = 180

8x = 180 - 20

8x = 160

x = 160 / 8

x = 20

Angle F is an opposite angle to angle D. Therefore,

∠D = ∠F

5x - 8 = 5(20) - 8 = 100 - 8 = 92°

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Answer 2

In parallelogram DEFG, angle F measures 92°

A parallelogram is a quadrilateral in which opposite sides are equal and parallel to each other.

In parallelogram DEFG:

∠D + ∠E = 180° (Consecutive angles are supplementary)

(5x - 8) + (3x + 28) = 180

8x + 20 = 180

8x = 160

x = 20°

∠D = 5x - 8 = 5(20) - 8 = 92°

∠D = ∠F = 92° (Opposite angles are congruent)

In parallelogram DEFG, angle F measures 92°

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