Question

Given: circle k(O), ED diameter, m∠OEF=32°, m EF=(2x+10)°. Find: x

Answer 1

Answer:

The value of x is $53\°$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc DF

we know that

The inscribed angle measures half that of the arc comprising

so

$m$

we have

$m$

substitute

$32\°=\frac{1}{2}(arc\ DF)\\ arc\ DF=64\°$

step 2

Find the measure of x

we know that

$arc\ DF+arc\ EF=180\°$ ---> is a semi circle

we have

$arc\ DF=64\°\\ arc\ EF=(2x+10)\°$

substitute

$64\°+(2x+10)\°=180\°\\ 2x\°=180\°-74\°\\ 2x\°=106\°\\ x=53\°$