Question

If the measure of arc LNM is 280 degrees, what is the value of y?

Answer 1

Given:

m(ar LNM) = 280°

To find:

The value of y.

Solution:

Complete angle = 360°

m(ar LNM) + m(ar LM) = 360°

280° + m(ar LM) = 360°

Subtract 280° from both sides.

280° + m(ar LM) - 280° = 360° - 280°

m(ar LM) = 80°

Inscribed angle is equal to the half of the intercepted arc.

`$\Rightarrow \angle LNM = (1)/(2) m (ar\ LM )`

`$\Rightarrow y= (1)/(2)(80^\circ )`

`$\Rightarrow y= 40^\circ`

The value of y is 40 degrees.