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Leviafan [203]
2 years ago
14

Please help with this arc equation.

Mathematics
1 answer:
boyakko [2]2 years ago
4 0

Answer:

Part 1) arc\ AB=49^o

Part 2) arc\ ABC=204^o

Part 3) arc\ BAC=156^o

Part 4) arc\ ACB=311^o

Step-by-step explanation:

Part 1) Find the measure of arc AB

we know that

arc\ AB=m\angle AOB ----> by central angle

we have

m\angle AOB=49^o

therefore

arc\ AB=49^o

Part 2) Find the measure of arc ABC

we know that

The central angle of complete circle is equal to 360 degrees

so

arc\ ABC=360^o-107^o-49^o=204^o

Part 3) Find the measure of arc BAC

we know that

arc\ BAC=arc\ BA+arc\ AC ----> by angle addition postulate

we have

arc\ BA=49^o ---> by central angle

arc\ AC=107^o ---> by central angle

so

arc\ BAC=49^o+107^o=156^o

Part 4) Find the measure of arc ACB

we know that

The central angle of complete circle is equal to 360 degrees

so

arc\ ACB=360^o-arc\ AB

substitute

arc\ ACB=360^o-49^o=311^o

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