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:

the correct option is d. 54°

step-by-step explanation:

for better understanding of the solution, see the attached figure :

given : cd and de are tangent to the circle. measure of arc ac = 126°

to find : measure of ∠cde

solution : measure of arc ac = 126°

⇒ ∠cae = 126°

now, as radius is perpendicular to the tangent of the circle

⇒ ∠aed = 90°

similarly, ∠acd = 90°

now, in quadrilateral sum of all the angles is 360°

⇒ sum of all the angles of quadrilateral aedc is 360°

⇒ ∠aed + ∠acd + ∠cae + ∠cde = 360°

⇒ 90° + 90° + 126° + ∠cde = 360°

⇒ 306° + ∠cde = 360°

⇒ ∠cde = 54°

hence, the measure of angle cde = 54°

therefore, the correct option is d. 54°