A geometry problem by Mehul Chaturvedi
Find The value of Angle DAE
The answer is 45.
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3 solutions
L
e
t
p
,
q
,
r
b
e
i
n
t
e
g
e
r
s
,
s
u
c
h
t
h
a
t
p
2
+
q
2
=
r
2
(
.
.
P
y
t
h
a
g
o
r
e
a
n
t
r
i
p
l
e
s
.
.
)
.
A
n
d
Δ
A
B
C
9
0
−
4
5
−
4
5
.
C
B
d
i
v
i
d
e
d
s
u
c
h
t
h
a
t
C
D
:
D
E
:
E
C
:
:
p
:
r
:
q
.
T
h
e
n
∠
E
A
D
=
4
5
o
.
I
n
t
h
i
s
p
r
o
b
l
e
m
C
D
:
D
E
:
E
C
:
:
p
:
r
:
q
:
:
3
:
5
:
4
.
I
a
m
n
o
t
g
o
o
d
a
t
t
h
e
o
r
y
o
f
n
u
m
b
e
r
s
.
I
s
t
h
e
r
e
a
n
y
p
r
o
o
f
a
l
r
e
a
d
y
?
M
y
p
r
o
o
f
i
s
a
s
u
n
d
e
r
.
W
e
s
a
w
∠
E
A
D
=
a
t
a
n
s
2
−
r
P
∗
r
Q
r
s
.
s
2
−
r
P
∗
r
Q
=
s
2
−
2
1
∗
(
s
−
p
)
(
s
−
q
)
.
=
−
p
∗
q
+
2
1
∗
(
p
+
q
+
r
)
(
p
+
q
)
=
2
1
∗
(
p
2
+
q
2
+
r
∗
(
p
+
q
)
)
=
2
1
∗
(
r
2
+
r
∗
(
p
+
q
)
=
r
∗
2
1
∗
(
p
+
q
+
r
)
=
r
s
.
∴
∠
E
A
D
=
a
t
a
n
(
1
)
=
4
5
∗
o
.
by ratio and proportion, ∠ A B D = 8 1 3 5 ∘ ∠ A D E = 4 5 ∘ ∠ A E C = 8 2 2 5 ∘
"by ratio and proportion" can you please explain what is this ratio !! How do you get the angles ? Thanks.