Question

Given: circle k(O), m

Answer 1

Answer:

$m$

Step-by-step explanation:

step 1

Find the measure of angle M.E.F

we know that

In an inscribed quadrilateral opposite angles are in fact supplements for each other

so

$m$

$m$

step 2

Find the measure of arc M.A.F

we know that

The inscribed angle measures half that of the arc comprising

so

$m$

we have

$m$

substitute

$105\°=\frac{1}{2}(arc\ M.A.F)$

$arc\ M.A.F=210\°$

step 3

Find the measure of arc A.F

$arc\ M.A.F=arc\ A.M+arc\ A.F$

we have

$arc\ M.A.F=210\°$

$arc\ A.M=125\°$

substitute

$210\°=125\°+arc\ A.F$

$arc\ A.F=210\°-125\°=85\°$

step 4

Find the measure of angle A.M.E

we know that

The inscribed angle measures half that of the arc comprising

so

$m$

we have

$arc\ A.F.E=arc\ A.F+arc\ E.F=85\°+31\°=116\°$

substitute

$m$