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

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calculista

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

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

we have

[tex]m\angle NQM=103^o[/tex]

substitute

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

[tex]206^o=arc\ MN+arc\ LP[/tex] ----> equation A

Remember that

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

so

[tex]arc\ LP=arc\ MN+30^o[/tex] ----> equation B

substitute equation B in equation A

[tex]206^o=arc\ MN+arc\ MN+30^o[/tex]

[tex]2arc\ MN=206^o-30^o\\2arc\ MN=176^o\\arc\ MN=88^o[/tex]

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abidemiokin

The measure of MN is 88 degrees

Circle geometry

From the diagram shown, the formula expressed below will be used to determine the measure of MN.

<NMQ = 1/2(arcLP + arcMN)

If the measure of LP is 30 degrees more than the measure of MN, then;

arcLP = 30 + arcMN

<NMQ = 1/2(30 + arcMN + arcMN)

2(103) = 30 + 2arcMN

206 - 30 = 2arcMN
arcMN = 88 degrees

Hence the measure of MN is 88 degrees

Learn more on circle geometry here: https://brainly.com/question/26594685

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