find the measures of each angle of a parallelogram

Question

The measure of one interior angle of a parallelogram(x) is 30º more than two times the measure of another angle(y). Find the measure of each angle of the parallelogram.

Answer 1

In a parallelogram, we know the following about the angles.

 

1) Opposite angles have the same measure.

2) The sum of the measures of two adjacent angles is 180

3) The sum of the measures of all 4 angles is 360

 

The first angle is denoted y

The second angle is 2y+30

 

From 2) above, (2y+30) + y = 180

or

2[(2y+30) + y] = 360

 

Using either of these equations

3y + 30 = 180

3y = 150

y = 50

2y + 30 = 2(50) + 30 = 130

 

So the smaller angle, y = 50º 

The angle opposite y is also 50º 

The other two angles measures 130º each.

Answer 2

Consecutive angles of a parallelogram are supplementary

 

y represents the "other" angle

2y + 30 represents the interior angle

 

y + 2y + 30 = 180           combine

3y + 30 = 180                 subtract 30 from both sides

3y = 150                         divide both sides by 3

y = 50

 

Two angles are 50° and two angles are 130°.