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vova2212 [387]
3 years ago
11

Find the measure of ∠ECB. Circle A is intersected by line CD at points D and E and line CB at point B, forming angle ECB outside

of the circle, the measure of angle ECB is x plus 10 degrees, arc EB is 6x plus 6 degrees, and arc DB 146 degrees.
Mathematics
2 answers:
goldfiish [28.3K]3 years ago
6 0

Answer:

its 45

Step-by-step explanation:

lubasha [3.4K]3 years ago
3 0

Answer:

m\angle ECB=50^o

Step-by-step explanation:

we know that

The measure of the external angle is the semi-difference of the arches it covers

so

In this problem

m\angle ECB=\frac{1}{2}(arc\ EB-arc\ DB)

substitute the given values

(x+10)^o=\frac{1}{2}((6x+6)^o-146^o)

solve for x

2x+20=6x-140\\6x-2x=20+140\\4x=160\\x=40

Find the measure of ∠ECB

substitute the value of x

m\angle ECB=(40+10)=50^o

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