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
