Lines cd and ce are tangent to circle a. if m∠dae = 130°, what is the measure of ∠dce?
230 degrees
130 degrees
100 degrees
50 degrees

The measure of ∠DCE is 50 degrees

Step-by-step explanation:

step 1

Find the measure of minor arc DE

we have

m∠DAE = 130°

we know that

m∠DAE=minor arc DE > by central angle

therefore

minor arc DE=130°

step 2

Find the measure of major arc DE

we know that

minor arc DE+major arc DE=360°

we have

minor arc DE=130°

substitute

130°+major arc DE=360°

major arc DE=360°-130°=230°

step 3

Find the measure of ∠DCE

we know that

The measurement of the outer angle is the semi-difference of the arcs which comprises

so

m∠DCE=(1/2)[major arc DE-minor arc DE]

substitute the values

m∠DCE=(1/2)[230°-130°]=50°

answer: 0+0=0

step-by-step explanation:

that is the only answer that can make 0

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