Respuesta :
Answer:
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:
The interior angles of the parallelogram are 21° and 159° respectively.
What is parallelogram?
A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.
In a parallelogram opposite interior angles are equal and the angles on the same side of the traversal are supplementary (i.e) 180°
For the given situation,
The measure of one interior angle be [tex]x[/tex] and
Another angle was given as [tex]9x-30[/tex]°
⇒[tex]x+9x-30[/tex]°[tex]=180[/tex]°
⇒[tex]10x=180[/tex]°[tex]+30[/tex]°
⇒[tex]10x=210[/tex]°
On dividing [tex]10[/tex] on both sides,
⇒[tex]\frac{10x}{10}=\frac{210}{10}[/tex]
⇒[tex]x=21[/tex]°
So, another angle is [tex]9x-30[/tex] = [tex]9[/tex]×[tex]21-30[/tex]
⇒[tex]189-30[/tex]
⇒[tex]159[/tex]°
Hence we can conclude that the interior angles of the parallelogram are 21° and 159°.
Learn more about the interior angle of parallelogram here
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