The Triangle Sum Theorem states that the sum of the angles of a triangle equal 180°.
Therefore,
45° + 62° + k = 180
107° + k = 180
k = 73°
The value of k is 73°
Check the forward differences of the sequence.
If
, then let
be the sequence of first-order differences of
. That is, for n ≥ 1,

so that
.
Let
be the sequence of differences of
,

and we see that this is a constant sequence,
. In other words,
is an arithmetic sequence with common difference between terms of 2. That is,

and we can solve for
in terms of
:



and so on down to

We solve for
in the same way.

Then



and so on down to


Let
x-----> the measure of the angle formed by the wooden fence and grass
we know that
in a right triangle
tan x=opposite side angle x/adjacent side angle x
opposite side angle x=13 ft
adjacent side angle x=21 ft
so
tan x=13/21x=arc tan (13/21)-----> x=31.76°------> x=32°
the answer is
32 degrees