Question

Need a little help. Lines CD and DE are tangent to circle A shown below: 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?
126°

63°

117°

54°

Answer 1

Its not 63 because I got that wrong

Answer 2

Answer:

The measure of ∠CDE=54°

Step-by-step explanation:

Given:- Lines CD and DE are tangent to a circle A.

Lines CD and DE are tangents to circle A and intersect at point D.

Arc measures CE = 126°=∠COE

Let o be the centre of circle A

Meet OC and OE which are radius of given circle A.

Now , we know that radius is perpendicular to the tangent.

Therefore, the angle∠OCD=90° and ∠OED=90°

In quadrilateral OCDE

∠OCE+∠OED+∠CDE+∠COE=360°  ( sum of angles of a quadrilateral=360°)

90+90+∠CDE+126=360

∠CDE=360-306

∠CDE=54°

Therefore, the measure for the angle CDE is 54°.