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ladessa [460]
2 years ago
14

Lines CD and DE are tangent to circle A as shown below: Lines CD and DE are tangent to circle A and intersect at point D. Arc CE

measures 130 degrees. Point B lies on circle A. If arc CE is 130°, what is the measure of ∠CDE?

Mathematics
2 answers:
Mice21 [21]2 years ago
5 0
The correct option for this question would be 50 degrees
dangina [55]2 years ago
5 0

Answer:

The measure of ∠CDE is 50°.

Step-by-step explanation:

Given information: Lines CD and DE are tangent to circle A. Arc CE measures 130 degrees.

According to the tangle to a circle property, the tangent of circle is perpendicular to the radius at the point of tangency.

It means ∠ACD and ∠AED are right angles.

The measure of arc CE is 130° it means the central angle of arc CE is 130°.

\angle CAE=130^{\circ}

According to the angle sum property, the sum of interior angles of a quadrilateral is 360°.

\angle ACD+\angle AED+\angle CAE+\angle CDE=360^{\circ}

90^{\circ}+90^{\circ}+130^{\circ}+\angle CDE=360^{\circ}

310^{\circ}+\angle CDE=360^{\circ}

\angle CDE=360^{\circ}-310^{\circ}

\angle CDE=50^{\circ}

Therefore the measure of ∠CDE is 50°.

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