Question

In the diagram of circle A, what is m∠LMN?

Answer 1

360-270=90
(270-90)/2
180/2=90°

Answer 2

`m\angle LMN=90^(O)`

Explanation:

We know that the outside angle formed between two tangents of a circle can be found by taking half of difference of bigger arc angle and smaller arc angle.

We can express it as:

`m\angle LMN=\frac{m\widehat{LN}_(Bigger)-m\widehat{LN}_(Smaller)}{2}`

From the given diagram, we get:

`m\widehat{LN}_(Bigger)=270\\m\widehat{LN}_(Smaller)=360-270=90`

Upon substituting these values in the formula, we get:

`m\angle LMN=(270-90)/(2)=(180)/(2)=90\\m\angle LMN=90^(0)`