The measure of one interior angle of a parallelogram is 30 degrees less than 9 times the measure of another angle. Find the measure of each angle.

The interior angles of the parallelogram are either:

XXX

{

159

∘

,

21

∘

,

159

∘

,

21

∘

}

or

XXX

{

3

3

4

∘

,

176

1

4

∘

,

3

1

4

∘

,

176

1

4

∘

}

Explanation:

Case 1: The given relation applies to consecutive angles

Consecutive angles of a parallelogram add up to  

180

∘

Let  

a

and  

b

be consecutive angles (measured in degrees) such that the given relation holds:

XXX

a

=

9

b

−

30

and since  

a

+

b

=

180

→

b

=

180

−

a

XXX

a

=

9

(

180

−

a

)

−

30

=

1620

−

9

a

−

30

=

1590

−

9

a

XXX

10

a

=

1590

XXX

a

=

159

and

XXX

b

=

180

−

a

=

21

Case 2: The given relation applies to opposite angles

Opposite angles of a parallelogram are equal.

Let  

a

be the measure (in degrees) of the referenced opposite angles (and  

b

be the measure of the other two angles:  

a

+

b

=

180

)

We are told

XXX

a

=

9

a

−

30

Therefore

XXX

−

8

a

=

−

30

XXX

a

=

3

3

4

XXX

b

=

180

−

a

=

176

1

4

Answer link

EZ as pi

Sep 25, 2016

The angles are  

21

°

,

159

°

,

21

°

,

159

°

Explanation:

In a parallelogram, there are only two sizes of angle - two are acute and two are obtuse.

Opposite angles are equal .

Consecutive angles are supplementary because they are co-interior angle on parallel lines.

An additional solution to the one given by Alan P is using the fact that the sum of the interior angles of a parallelogram is 360°.

Let one angle be  

x

The size of the other angle is given by  

9

x

−

30

2

x

+

2

(

9

x

−

30

)

=

360

←

sum of the angles is 360°

2

x

+

18

x

−

60

=

360

20

x

=

420

x

=

21

°

The obtuse angles are each  

180

−

21

=

159

°

The other option where the given angle is the opposite angle is described is well explained by Alan P.

Step-by-step explanation:

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.