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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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Step-by-step explanation:

Given that,

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To find,

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Firstly we'll find the base radius of the cylinder.

\longmapsto\rm{V_{(Cylinder)} = \pi r^2h}\\

<u>Accordi</u><u>ng</u><u> </u><u>to</u><u> </u><u>the</u><u> </u><u>qu</u><u>estion</u><u>,</u>

\longmapsto\rm{616= \dfrac{22}{7} \times r^2 \times 4}\\

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\longmapsto\rm{4312 = 88 \times r^2 }\\

\longmapsto\rm{\cancel{\dfrac{4312}{88}} =  r^2 }\\

\longmapsto\rm{49 =  r^2 }\\

\longmapsto\rm{\sqrt{49} =  r }\\

\longmapsto\rm{7 \; cm =  r }\\

Now,

\longmapsto\rm{Diameter = 2r }\\

\longmapsto\rm{Diameter = 2(7 \; cm) }\\

\longmapsto\bf{Diameter = 14 \; cm}\\

The required answer is 14 cm.

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