Question

In ⊙L, m∠NMO=9x−3 and m∠NPO=4x+12. Find mNO.

Answer 1

48°

Explanation:

I'm actually just assuming that you mean arc NO. Proceeding with that...

Angle NMO is an inscribed angle which intercepts arc NO. Angle NPO is also an inscribed angle that intercepts arc NO. Because they both intercept the same arc, both inscribed angles have the same measure. Therefore,

9x - 3 = 4x + 12

Solving for x:

5x = 15

x = 3. Plug 3 in for x in either one of the equations to get that angles NMO and NPO measure

9(3) - 3 = 24°

The rule is that inscribed angles measure HALF of the arcs they intercept, so the measure of arc NO is 48°

Answer 2

arc NO has measure 48

Explanation:

We assume all measures are in consistent units (degrees or something similar). The two inscribed angles intercept the same arc, so are congruent:

9x -3 = 4x +12

5x = 15 . . . . . . . add 3-4x

x = 3 . . . . . . . . . divide by 5

The measure of the inscribed angle is then ...

4x +12 = 4(3) +12 = 24

That is half the measure of the arc, so the measure of arc NO is ...

arc NO = 2·24 = 48