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Introduction to Circles
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In circle o, AC and BD are diameters.
What is mBC?
(3x - 70°
50°
80°
100
130°
o o
(x + 10)

Respuesta :

luisejr77

Answer: OPTION D. [tex]130\°[/tex]

Step-by-step explanation:

The missing figure is attached.

As you can observe in the figure AC and BD intersect each other at the point O. Then, you can identify that:

 [tex]\angle AOB =\angle COD\\\\\angle AOD =\angle BOC[/tex]

Subsitute values:

 [tex]\angle AOB =\angle COD\\\\3x - 70=x + 10[/tex]

Solve for "x":

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

Therefore:

[tex]\angle AOB =arc\ AB=3(40) - 70=50\°\\\\\angle COD=arc\ CD=40 + 10 =50\°[/tex]

They are 360 degrees in a circle. Then:

[tex]arc\ AB+arc\ CD+arc\ BC+arc\ AD=360\°[/tex]

Substituting values and solving for arc BC, you get:

[tex]50\°+50\°+arc\ BC+arc\ BC=360\°\\\\arc\ BC=\frac{260\°}{2}\\\\arc\ BC=130\°[/tex]

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abidemiokin

The measure of arcBC if AC and BD are diameters is 130 degrees

Circle geometry

From the given diagram, the given angles are vertically opposite, that is they are equal to each other. Mathematically;

3x - 70 =x +10

3x - x = 10 +70

2x =80

x = 40

Since the sum of angle on a straight line is 180 degrees, hence;

arc BC + arc CD = 180

arcBC+ x + 10 = 180

arcBC + 50 = 180

arcBC = 180 - 50

arc BC=  130degrees

Hence the measure of arcBC if AC and BD are diameters is 130 degrees

Learn more on geometry here: https://brainly.com/question/25766008

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