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posledela
3 years ago
7

In the figure below, XZ is a diameter of circle A what is the arc measure of YZ in degrees

Mathematics
1 answer:
diamong [38]3 years ago
8 0

Answer:

arc YZ = 59°

Step-by-step explanation:

Since XZ is a diameter then ∠ XAZ = 180°

∠XAY + ∠ YAZ = ∠ XAZ , substitute values

11w + 5w + 4 = 180, that is

16w + 4 = 180 ( subtract 4 from 180 )

16w = 176 ( divide both sides by 16 )

w = 11

Thus ∠ YAZ = 5w + 4 = 5(11) + 4 = 55 + 4 = 59°

The arc YZ is the measure of the central angle it subtends, thus

arc YZ = 59°

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