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Margaret [11]
3 years ago
14

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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