what is the measure of one internal angle of a regular pentagon?
Answers
Answer:
180 degree
Step-by-step explanation:
The total interior angles of a pentagon are 540 degrees The total interior angles of a pentagon = 540° Each time we add a side (triangle to square, square to pentagon, pentagon to hexagon ) we add another 180°.
Answer:
Consider this regular pentagon
A
B
C
D
E
.
Let us join vertices
A
C
and
E
C
as shown to form three triangles as shown. I have used letters
a
,
b
,
c
,
d
,
e
,
f
,
g
,
h
,
i
to represent internal angles of triangles for sake of simplicity.
Since the sum of interior angles of a triangle is
180
o
,
In
△
A
B
C
,
b
+
c
+
d
=
180
o
In
△
A
C
E
,
a
+
e
+
i
=
180
o
In
△
E
C
D
,
h
+
f
+
g
=
180
o
Sum of interior angles of the pentagon is
a
+
b
+
c
+
d
+
e
+
f
+
g
+
h
+
i
=
(
b
+
c
+
d
)
+
(
a
+
e
+
i
)
+
(
h
+
f
+
g
)
=
180
o
+
180
o
+
1
80
o
[using the above three results]
=
540
o
i
.
e
.
∠
A
+
∠
B
+
∠
C
+
∠
D
+
∠
E
=
540
o
Since it is a regular octagon,
∠
A
=
∠
B
=
∠
C
=
∠
D
=
∠
E
⇒
∠
A
+
∠
A
+
∠
A
+
∠
A
+
∠
A
=
540
o
⇒
5
⋅
∠
A
=
540
o
⇒
∠
A
=
540
5
=
108
o
=
∠
B
=
∠
C
=
∠
D
=
∠
E
Hence internal angle of a regular pentagon is
108
o
.
Step-by-step explanation:
pls mark me as brainiest