Question

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?

Answer 1

The correct option for this question would be 50 degrees

Answer 2

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°.