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3 years ago

Introduction to Circles

Mathematics

1 answer:

shepuryov [24]3 years ago

5 0

Answer: OPTION D. $130\°$

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:

$\angle AOB =\angle COD\\\\\angle AOD =\angle BOC$

Subsitute values:

$\angle AOB =\angle COD\\\\3x - 70=x + 10$

Solve for "x":

$3x-x=70 + 10\\\\2x=80\\\\x=40$

Therefore:

$\angle AOB =arc\ AB=3(40) - 70=50\°\\\\\angle COD=arc\ CD=40 + 10 =50\°$

They are 360 degrees in a circle. Then:

$arc\ AB+arc\ CD+arc\ BC+arc\ AD=360\°$

Substituting values and solving for arc BC, you get:

$50\°+50\°+arc\ BC+arc\ BC=360\°\\\\arc\ BC=\frac{260\°}{2}\\\\arc\ BC=130\°$

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