Respuesta :

joseaaronlara

Answer:

The answer to your question is x = 40; A = 46

Step-by-step explanation:

Data

∠B = 3x + 14

∠C = x + 6

Property of parallelograms: Consecutive angles are supplementary

That means that ∠B + ∠C = 180°

Substitution

                         3x + 14 + x + 6 = 180

Simplification

                         4x = 180 - 14 - 6

                         4x = 180 -20

                          4x = 160

                            x = 160/4

Result

                            x = 40    

And ∠A = 40 + 6     Because Opposite angles are congruent

             = 46°                        

Answer:

Step-by-step explanation:

The plane figure shown in the diagram is a parallelogram. In a parallelogram, opposite sides are equal and parallel.

The consecutive angles in a parallelogram are supplementary. This means that the sum of the consecutive angles of the parallelogram is 180 degrees.

(3x + 14)° and (x + 6)° are consecutive angles. Therefore,

(3x + 14) + (x + 6) = 180

3x + 14 + x + 6 = 180

3x + x + 14 + 6 = 180

4x + 20 = 180

4x = 180 - 20

4x = 160

x = 160/4

x = 40

Angle C = x + 6 = 40 + 6

Angle C = 46°

Opposite angles of a parallelogram are equal. Therefore,

Angle A = Angle C = 46°

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