If one angle in a parallelogram is twice the measure of the consecutive angle, what are the measures of the angles?
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The measure of the angles of a parallelogram are ∠A = 120°, ∠B = 60°, ∠C = 120° and ∠D = 60°.

Step-by-step explanation:

The consecutive angles of a parallelogram are supplementary, i.e. they sum up to 180°.

Consider the parallelogram ABCD.

∠A and ∠D and ∠B and ∠C are consecutive angles.

In a parallelogram opposite angles are equal.

That is: ∠A = ∠C and ∠B = ∠D.

Using the provided information, suppose ∠A = 2 × ∠D.

Compute the value of ∠A and ∠D as follows:

∠A + ∠D = 180°

2∠D + ∠D = 180°

3∠D = 180°

∠D = 60°

Then the measure of ∠A is:

∠A = 2∠D

     = 2 × 60°

     = 120°

Now the measure of ∠B and ∠C are:

∠C = ∠A = 120°

∠B = ∠D = 60°

Thus, the measure of the angles of a parallelogram are ∠A = 120°, ∠B = 60°, ∠C = 120° and ∠D = 60°.

the measures of the angles are 120 degrees and 60 degrees.

Step-by-step explanation:

In a parallelogram, the opposite angles are equal and the consecutive angles are supplementary. This means that the sum of the angles is 180 degrees.

Let x represent the measure of one of the angles of the parallelogram. The consecutive angle would be 180 - x

If one angle in a parallelogram is twice the measure of the consecutive angle, it means that

x = 2(180 - x)

x = 360 - 2x

2x + x = 360

3x = 360

x = 360/3

x = 120 degrees

The other angle is

180 - 120 = 60 degrees

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