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Lines CD and DE are tangent to circle A shown below: If Arc CE is 112°, what is the measure of ∠CDE? a 124° b 136° c 68° d 56°

Lines CD and DE are tangent to circle A shown below If Arc CE is 112 what is the measure of CDE a 124 b 136 c 68 d 56 class=

Respuesta :

jcherry99

Answer:

C

Step-by-step explanation:

The central angle of this is 112 degrees. That is CAE is 112 degrees. That being the case, CDE is 90 + 90 + 112  = 292 Tangents make a 90 degree angle with the center of the circle.

CDE = 360 - 292 = 68

C

abidemiokin

The measure of ∠CDE is 68degrees

This question bothers on circle geometry;

From the diagram, we can see that ACDE will form a quadrilateral. Since the sum of angles of a quadrilateral is 360degrees, hence;

[tex]<CDE + arcCE+<C+<E=360[/tex]

From the diagram, since CD and DE are both tangential to the circle at point C and E, this shows that <E = <E = 90°

substituting the given values in the formula;

[tex]<CDE+112+90+90=360\\<CDE + 292=360\\<CDE=360-292\\<CDE =68^0[/tex]

Hence the measure of ∠CDE is 68 degrees

Learn more on circle geometry: https://brainly.com/question/24357871

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