Part (i)
Angle DBA = 44
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Reason:
Angle CBA is a right angle (thales theorem), so angle DBA must add to DBC to get 90 degrees. In other words, we solve x+46 = 90 to get x = 44.
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Part (ii)
Angle DAC = 46
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Reason:
Both inscribed angles DAC and DBC subtend the same arc (minor arc DC), so the inscribed angles are congruent.
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Part (iii)
Angle BCE = 74
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Reason:
Angle BDC is 28 degrees since angle BAC is also 28 degrees (similar reasoning as part ii above). Let y = angle BCD
Focus on triangle BCD. The three interior angles add to 180
B+C+D = 180
46+y+28 = 180
y+74 = 180
y = 180-74
y = 106
Then subtract 180 from this to get the exterior angle BCE
angle BCE = 180-(angle BCD)
angle BCE = 180-y
angle BCE = 74
Or as a shortcut, you could use the remote interior angle theorem
angle BCE = (angle BDC) + (angle DBC)
angle BCE = (28) + (46)
angle BCE = 74