9514 1404 393
Answer:
Explanation:
The relevant relations are ...
- the sum of the arcs of a circle is 360°
- an inscribed angle subtends an arc twice its measure
These give rise to two equations. (x and y are in degrees)
6y +6y +4x = 360
6y = 2(2x)
Substituting the latter into the former gives ...
6y +6y +6y = 360
y = 20 . . . . . . . . . . . . divide by 18
Then using this in the second equation, we have ...
6(20) = 4x
30 = x . . . . . . . . divide by 4
The measures of x and y are 30° and 20°, respectively.