Question

Given: circle k(O), mAM=125°, mEF=31°, m∠MAF=75° Find: m∠AME

Answer 1

Answer:

The measure of angle A.M.E is $58\°$

Step-by-step explanation:

step 1

Find the measure of arc M.E

we know that

The inscribed angle is half that of the arc it comprises.

$m$

we have

$m$

$arc\ E.F=31\°$

substitute the values

$75\°=\frac{1}{2}(arc\ M.E+31\°)$

$150\°=(arc\ M.E+31\°)$

$arc\ M.E=150\°-31\°=119\°$

step 2

Find the measure of arc A.F

we know that

$arc\ M.E+arc\ E.F+arc\ A.F+arc\ A.M=360\°$ -----> by complete circle

substitute the values

$119\°+31\°+arc\ A.F+125\°=360\°$

$119\°+31\°+arc\ A.F+125\°=360\°-275\°=85\°$

step 3

Find the measure of angle A.M.E

we know that

The inscribed angle is half that of the arc it comprises.

$m$

substitute the values

$m$