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

HEY YA'll - I really need help with this - I missed class and have NO idea...

BRAINLIEST 10 PTS 5 Stars amp Thanks for first correct answerGiven circle kO ED diameter mOEF32 measure of arc EF2x10 Find xHEY YAll I really need help with thi class=

Respuesta :

calculista

Answer:

[tex]x=53\°[/tex]

Step-by-step explanation:

step 1

Find the measure of arc DF

we know that

[tex]arc\ DF+arc\ EF=180\°[/tex] ----> Equation A

Because the diameter DE divide the circle into two equal parts

we know that

The inscribed angle measures half that of the arc comprising

[tex]m<OEF=\frac{1}{2}(arc\ DF)[/tex]

substitute the given value

[tex]32\°=\frac{1}{2}(arc\ DF)[/tex]

[tex]64\°=(arc\ DF)[/tex]

[tex]arc\ DF=64\°[/tex]

step 2

Find the measure of arc EF

[tex]arc\ DF+arc\ EF=180\°[/tex]

substitute the measure of arc DF

[tex]64\°+arc\ EF=180\°[/tex]

[tex]arc\ EF=180\°-64\°=116\°[/tex]

step 3

Find the value of x

we have

[tex]arc\ EF=116\°[/tex]

[tex]arc\ EF=(2x+10)\°[/tex]

equate the equations

[tex](2x+10)\°=116\°[/tex]

[tex]2x=116\°-10\°=106\°[/tex]

[tex]x=53\°[/tex]

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