In circle O, AC and BE are diameters. The measure of arc DC is 50°. What is the measure of EBC?
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Answer:
Using properties of parallelogram and angle sum property of a triangle in the figure as shown below in the attachment
In parallelogram ABCD, AC is a diagonal.
Given: and
As, we know that opposite angles in parallelogram are equal.
therefore,
Now, in ΔADC
Sum of the measures of angles in a triangle is 180 degree.
Substituting the values of and
we have;
or
Subtract from both sides we get
Therefore, the measure of angle CAD is .
