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Olin [163]
3 years ago
14

In the diagram of circle O, mNQM  103 . If the measure of LP is 30 more than the measure of MN ,  then determine the measur

e of MN . Show how you arrived at your answer.

Mathematics
1 answer:
IceJOKER [234]3 years ago
7 0

Answer:

The measure of arc MN is 88 degrees

Step-by-step explanation:

The complete question in the attached figure

we know that

The measure of the interior angle is the semi-sum of the arches that comprise it and its opposite

so

m\angle NQM=\frac{1}{2}(arc\ MN+arc\ LP)

we have

m\angle NQM=103^o

substitute

103^o=\frac{1}{2}(arc\ MN+arc\ LP)

206^o=arc\ MN+arc\ LP ----> equation A

Remember that

The measure of arc LP is 30 degrees more than the measure of arc MN

so

arc\ LP=arc\ MN+30^o ----> equation B

substitute equation B in equation A

206^o=arc\ MN+arc\ MN+30^o

2arc\ MN=206^o-30^o\\2arc\ MN=176^o\\arc\ MN=88^o

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