Question

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.

Answer 1

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

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

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