How do I find the base angle of an isosceles trapezoid with bases 10 and 18 in length and a leg that is 8 in length?
Answers
Answer:
×
60
x
Degrees
Explanation:
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×
|
E
F
|
=
|
D
C
|
×
×
x
=
10
x
in
×
|
A
D
|
=
|
B
C
|
×
×
×
×
×
x
(isosceles trapezoid),
×
|
D
E
|
=
|
C
F
|
×
×
×
×
×
x
(isosceles trapezoid),
×
m
(
∠
A
D
E
)
=
m
(
∠
B
C
F
)
×
x
(isosceles trapezoid),
SAS Postulate
: Two sides in a triangle have the same length as two sides in the other triangle, and the included angles have the same measure. Therefore
×
Δ
A
D
E
and
×
Δ
B
C
F
are congruent:
×
Δ
A
D
E
=
Δ
B
C
F
×
|
A
B
|
=
18
x
in
×
×
×
×
×
×
×
×
×
×
×
(base length)
⇒
|
A
E
|
+
|
E
F
|
+
|
F
B
|
=
18
x
in
×
×
×
×
×
x
(base length)
⇒
|
A
E
|
+
|
E
F
|
+
|
A
E
|
=
18
x
in
×
×
×
×
×
(SAS Postulate)
⇒
|
A
E
|
+
10
+
|
A
E
|
=
18
⇒
|
A
E
|
+
10
+
|
A
E
|
−
10
=
18
−
10
⇒
1
2
×
2
×
|
A
E
|
=
1
2
×
8
⇒
|
A
E
|
=
4
×
cos
m
(
∠
D
A
E
)
=
8
4
×
×
×
×
×
x
=
1
2
⇒
cos
m
(
∠
D
A
E
)
=
cos
60
⇒
arccos
cos
m
(
∠
D
A
E
)
=
arccos
cos
60
⇒
m
(
∠
D
A
E
)
=
60
Step-by-step explanation: