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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.

Respuesta :

calculista

Answer:

[tex]m\angle ECB=50^o[/tex]

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

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

substitute the given values

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

solve for x

[tex]2x+20=6x-140\\6x-2x=20+140\\4x=160\\x=40[/tex]

Find the measure of ∠ECB

substitute the value of x

[tex]m\angle ECB=(40+10)=50^o[/tex]

braylonverx387

Answer:

A. 25

Step-by-step explanation:

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