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line cd in DE are tangent to circle a shown below ifCE is 130° what is the measure of angle CDE
20°
40°
42.5°
50°

line cd in DE are tangent to circle a shown below ifCE is 130 what is the measure of angle CDE 20 40 425 50 class=

Respuesta :

akposevictor

Answer:

m<CDE = 50°

Step-by-step explanation:

Recall: when an angle is formed outside a circle by two tangents, the angle formed = ½(the difference between the measures of the intercepted arcs), based on the outside angles theorem.

This implies that:

m<CDE = ½(Arc CBE - Arc CE)

Arc CE = 130°

Arc CBE = 360° - 130° = 230°

Plug in the values

m<CDE = ½(230 - 130)

m<CDE = ½(100)

m<CDE = 50°

abidemiokin

The measure of angle m<CDE is 50 degrees

Circle geometry

From the diagram shown, the angle at the vertex is equal to half the difference of the angles at the intercepted arc.

Given

  • Angles at the arcs are 130 and 230 (360 - 130)
  • Angle at the vertex = m<CDE

m<CDE = 1/2(230-130)

m<CDE = 1/2(100)

m<CD = 50 degrees

Hence the measure of angle m<CDE is 50 degrees

Learn more on circle geometry here: https://brainly.com/question/24375372

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