Geometry Problem: Finding Angle in a Square with Given Angles

Solve for the unknown angle in a square ABCD with points E on AD and F on CD, given specific angles. Uses trigonometry and properties of squares.

Answer

Based on the image provided, we are given a square

with a point

on the side

and a point

on the side

. We are given that

and

. We need to find the angle

Let the side length of the square be

. Let the coordinates of the vertices be

, and

.
Point

lies on

, so its coordinates are

for some

.
In

, we have

and

.
Thus,

.
So, the coordinates of

are

Point

lies on

, so its coordinates are

for some

.
In

, we have

and

.
The length

.
Then,

.
So, the coordinates of

are

We want to find

. Let

.
In

, we have

We recognize that

is the value of

.
To verify:

Therefore,

Final Answer:

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