Question

lines cd and de are tangent to circle a, as shown below:

if \\(\widehat{ce}\\) is \\(110^\circ\\), what is the measure of \\(\angle cde\\)?

• \\(55^\circ\\)
• \\(70^\circ\\)
• \\(100^\circ\\)
• \\(125^\circ\\)

Explanation:

Determine the measure of the major arc CBE

$$ m(\widehat{CBE}) = 360^\circ - m(\widehat{CE}) = 360^\circ - 110^\circ = 250^\circ $$

Apply the Tangent-Tangent Angle Theorem

$$ m\angle CDE = \frac{m(\widehat{CBE}) - m(\widehat{CE})}{2} $$

$$ m\angle CDE = \frac{250^\circ - 110^\circ}{2} = \frac{140^\circ}{2} = 70^\circ $$

Answer:

• (A) \(55^\circ\)
• (B) \(70^\circ\) (Correct answer)
• (C) \(100^\circ\)
• (D) \(125^\circ\)