Question

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.

Answer 1

Answer:

its 45

Step-by-step explanation:

Answer 2

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

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