Junior high school mathematics problems

This topic is mainly to practice the knowledge of circle angle, especially the theorem: the circle angle of the same arc is half of the central angle.

Make an auxiliary line AD and extend the intersection of DO to F.

Analysis:

Because the arc corresponding to ∠x is AC, it is enough to find the circumferential angle corresponding to the arc AC ∠ADC degrees.

∠ADC consists of∠ ∠FDC (commonly known as 20) and∠ ADF, so the key is to understand the degree of∠ ADF.

Solution:

∵ In the isosceles? At OAB

∠ AOB = 120 (known, the corresponding arc is 120).

∴∠ado=( 180- 120)/2 = 30

∴ arc af = 60

It's also VIII

FDC = 20 (known)

∴ arc fc = 40

∴ arc AC= arc AF+ arc FC = 60+40 = 100

∴∠x = 50° (the circumferential angle of the same arc is half of the central angle)