Question

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

Answer 1

Answer:

$x=53$

Step-by-step explanation:

step 1

Find the measure of arc DF

we know that

The inscribed angle measures half that of the arc comprising

so

$m<OEF=\frac{1}{2}(arc\ DF)$

we have

$m<OEF=32\°$

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 half the circle

we have

$arc\ DF=64\°$

$arc\ EF=(2x+10)\°$

substitute

$64\°+(2x+10)\°=180\°$

$2x\°=180\°-74\°$

$2x\°=106\°$

$x=53$

Answer 2

The value of x for the angles of the inscribed circle is gotten as; x = 53°

What is the value of the angle in the circle?

Let us first find the angle subtended by the arc DF

From inscribed angle theorem, we know that the measure of an inscribed angle is half the measure of the intercepted arc. Thus;

m∠EOF = ¹/₂(arc DF)

Thus;

¹/₂(arc DF) = 32°

arc DF = 64°

From half circle theorem, we can say that;

arc DF + arc EF = 180°

Thus;

64 + 2x + 10 = 180

2x = 180 - 74

2x = 106

x = 53°

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