#### Answer

$m\angle{1} = 135^o
\\m\angle{2} = 45^o$

#### Work Step by Step

RECALL:
The total measurement of the angles of a polygon with $n$ sides is given by the formula:
$180^o(n-2)$
An octagon has 8 sides.
Thus, the sum of the angles inside an octagon is:
$=180^o(8-2)
\\=180^o(6)
\\=1080^o$
Since a regular octagon has 8 congruent interior angles, the measure of each interior angle can be found by dividing the sum of all the interior angles by the number of interior angles (which is 8).
Thus, each interior angle of a regular octagon measures:
$=\dfrac{1080^o}{8}
\\=135^o$
Thus, $m\angle{1}= 135^o$.
In the given figure, combining angles 1 and 2 form a straight line.
This means that the two angles are supplementary (sum is 180 degrees).
Therefore,
$m\angle{2} = 180^o - 135^o = 45^o$