, 22.06.2019 21:00 Tink2334

# If da is a diameter of circle z and m dzc=(2x) degrees, find m czb

M∠CZB = 73°.

Since DA is a diameter, all of the angles along either side of it will be supplementary (add to 180°).  This means that ∠DZC + ∠CZB + ∠BZA = 180°:

2x + 7x - 4 + 85 = 180

Combining like terms, we have:
9x + 81 = 180

Subtract 81 from both sides:
9x + 81 - 81 = 180 - 81
9x = 99

Divide both sides by 9:
9x/9 = 99/9
x = 11

To find the measure of ∠CZB, substitute 11 in for x:
m∠CZB = 7x - 4 = 7(11) - 4 = 77 - 4 = 73
We are given that
arc BD= arc BC
Therefore,
DY = CY
and
2x + 1 = 4x - 3
Solving for x
x = 2

Since AB = 6x + 1
The diameter is
6(2) + 1
= 13

D. 13

### Other questions on the subject: Mathematics

Mathematics, 21.06.2019 15:40, AM28
Brian, chris, and damien took a math test that had 20 questions. the number of questions brian got right is 14 more than the number of questions chris got right. damien correctly answered 2 less than the number of questions chris answered correctly. if brian and damien have the same score, which statement is true?