# 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°.