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In circle A shown below, BD with a line above is the diameter and the measure of arc CB is 54 degrees. What is the measure of angle DBC

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calculista
the complete question in the attached figure

we know that
the triangle ACB is an isosceles triangle
AC=AB----------> equals to the radius
so
∡ACB=∡CBA
the angle ∡CAB is equals to 54° by central angle
so
180°=54°+2*∡CBA--------> ∡CBA=[180-54]/2-----> 63°
∡CBA=63°
∡DBC=∡CBA-----------> ∡DBC=63°

the answer is
∡DBC=63°

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Answer:

Line segment BD is the diameter of Circle A. It is also the hypotenuse of the right triangle found inside circle A.

angle C = 90°

angle D = 54°/ 2 = 27°

angle B = 180° - 90° - 27° = 63°

The measure of ∡DBC is 63°

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