Question

This figure shows circle C with diameter LM and inscribed ∠LMN .

m∠LMN=32°



What is the measure of arc LMN?

Enter your answer in the box.

Answer 1

the answer is 296 degress

Answer 2

`296^(\circ)`

Explanation:

It is given that figure shows circle C with diameter LM and inscribed ∠LMN and m∠LMN=32° .

We know that the angle formed at the center is double the angle formed on the vertex that is an inscribed angle, thus on joining NC, we have

`{\angle}NCL=2({\angle}LMN)`

Substituting the given values, we have

`{\angle}NCL=2(32^(\circ))`

`{\angle}NCL=64^(\circ)`

Now,
`minor{\angle}LCN+major{\angle}LCN=360^(\circ)` (complete angle)

`major{\angle}LCN=296^(\circ)`

Therefore, the measure of the arc LMN is
`296^(\circ)`.