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Lines CD and DE are tangent to circle A, as shown below: If arc CE is 110°, what is the neasure of angle CDE?

A. 55°
B. 70°
C. 100°
D. 125°​

Lines CD And DE Are Tangent To Circle A As Shown Below If Arc CE Is 110 What Is The Neasure Of Angle CDE A 55 B 70 C 100 D 125 class=

Sagot :

Akposevictoridn

Answer:

B. 70°

Explanation:

Apply the Outside Angle Theorem which says the angle formed by two tangents outside a circle is equal to half of the difference of the intercepted arcs.

The intercepted arcs are:

m(CE) = 110°

m(CBE) = 360° - 110° = 250°

Thus:

m<CDE = ½(m(CBE) - m(CE))

Substitute

m<CDE = ½(250° - 110°)

m<CDE = ½(140°)

m<CDE = 70°

According to the Outside Angle Theorem,

The intercepted arcs are:

m(CE) = 110°

m(CBE) = 360° - 110° = 250°

Thus,

m<CDE = ½(m(CBE) - m(CE))

Substitute,

m<CDE = ½(250° - 110°)

m<CDE = ½(140°)

m<CDE = 70°

What is an angle ?

An angle is a figure in which two rays emerge from a common point. This point is called the vertex of the angle, and the two rays forming the angle are called its arms or sides. An angle which is greater than 180 degrees but less than 360 degrees is called a reflex angle.

Thus, option B is true, that angle CDE will be 70*.

Learn more about angle here,

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