Lines CD and DE are tangent to circle A:

Question

Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 126 degrees. Point B lies on circle A.

If arc CE is 126°, what is the measure of ∠CDE? (1 point)

126°

63°

117°

54°

Answer 1

To find the measure of ∠CDE, we can use the property that an angle formed by two tangent lines from the same external point (in this case, point D) is half the measure of the arc that lies in the opposite sector of the circle.

Here, arc CE measures 126 degrees. Therefore, the angle ∠CDE can be calculated as follows:

\[ \angle CDE = \frac{1}{2} \times \text{measure of arc CE} \]

\[ \angle CDE = \frac{1}{2} \times 126^\circ = 63^\circ \]

Thus, the measure of ∠CDE is 63°.