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In circle O, MP is a diameter. Circle O is shown. Line segment MP is a diameter. Line segment NO is a radius. If mArc NP is 6 more than 5 times the measure of Arc MN , what is mArc NP ?
139°, 145°, 151°, 174°
Solution:
Given MP is a diameter
mArc NP is 6 more than 5 times the measure of Arc MN
Let us assume
m arc MN = x
m arc NP = y
5x + 6 = y …………………….(a)
We know that the full arc of semi circle is 180°
x + y = 180 …………………..(b)
Putting eq(a) in eq(b)
⇒ x + (5x + 6) = 180
⇒ 6x + 6 = 180
⇒ 6x = 174
⇒ x = 29°
y = 151°
In circle O, MP is a diameter. Circle O is shown. Line segment MP is a diameter. Line segment NO is a radius. If mArc NP is 6 more than 5 times the measure of Arc MN , what is mArc NP ?
139°, 145°, 151°, 174°
Summary:
In circle O, MP is a diameter. Circle O is shown. Line segment MP is a diameter. Line segment NO is a radius. If mArc NP is 6 more than 5 times the measure of Arc MN , then mArc NP is 151°.
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