contestada

In the figure below, \overline{BD}
BD
start overline, B, D, end overline and \overline{AC}
AC
start overline, A, C, end overline are diameters of circle PPP.
What is the arc measure of \stackrel{\Huge{\frown}}{DBC}
DBC
⌢
D, B, C, start superscript, \frown, end superscript in degrees?
^\circ
∘
degrees

Respuesta :

calculista

Answer:

[tex]arc\ DBC=310^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the value of x

we know that

[tex]arc\ AB=arc\ DC[/tex] ----> by central angle (Remember that C is the center of the circle)

so

[tex](3x-70)^o=(x+10)^o[/tex]

solve for x

[tex]3x-x=10+70\\2x=80\\x=40[/tex]

step 2

Find the measure of arc BC

we know that

The diameter divide the circle into two equal arcs of measure 180 degrees each

so

[tex]arc\ AB+arc\ BC=180^o[/tex]

[tex](3(40)-70)^o+arc\ BC=180^o[/tex]

[tex]arc\ BC=180-120+70\\arc\ BC=130^o[/tex]

step 3

Find the measure of arc DBC

we know that

The measure of arc DBC is given by

[tex]arc\ DBC=arc\ DAB+arc\ BC[/tex]

we have

[tex]arc\ DAB=180^o[/tex] ---> because BD is a diameter of circle P

[tex]arc\ BC=130^o[/tex]

substitute

[tex]arc\ DBC=180^o+130^o=310^o[/tex]

Ver imagen calculista
mikaela4life051

Answer:

arc Measure for Bc is 147, arc measure for DBC is 213

Step-by-step explanation:

there are numerous variations of this question. the answer to this specific question is 213 degrees.  along with this, if you are looking for the answer to this question but just with the arc measure of BC, the answer is 147. Hope this helps!

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