Answer:
<h2>By angle sum property:</h2>BAC+ABC+BCA=180°
90°+45°+x=180°
135°+x=180°
x=45°=BCA
<h2>since BCA=ABC=<u> </u>45° each </h2><h2>therefore,</h2>
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 an
gle DBC
2 answers:
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°
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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