Answer:
Suppose that we have a circle of radius R.
The total perimeter of this circle will be:
P = 2*pi*R
Where pi = 3.14159...
Now, if we have a section of this circle with an angle A, the "chord" of this section will be:
C = (A/360°)*2*pi*R.
Where you can see that if A = 360° (so the section is the whole circle) the chord is equal to the perimeter.
In this particular case, the chord is equal to the radius of the circle, then we get:
C = R = (A/360°)*2*pi*R
We need to solve this for A.
R = (A/360°)*2*pi*R
We can divide both sides by R to get:
1 = (A/360°)*2*pi
Now we need to isolate A.
(360°/2*pi) = A = 57.3°
This would be the angle in the minor arc.
And the angle for the mayor arc would be the difference between the angle for a whole circle (360°) and the angle of this section (57.3°)
The angle for the major arc is:
A = 360° - 57.3° = 302.7°