Answer :
Answer:
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°.
Answer: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