In the diagram of circle a, what is m∠lmn?

Solution:

The angle between the two tangents (LM & LN) drawn from the external point to a circle i.e. is supplementary of the angle ∠LMN

∠MLA = 90°

∠MNA = 90°

Also,

External angle ∠LAN = 270°

Internal angle ∠LAN = 360° - 270° = 90°

By using angle sum property of quadrilateral, we get

∠LMN = 90°

This implies that the polygon LAMN is a square since adjacent sides are equal and all angles equal to 90°.

In the diagram of circle a, what is m∠lmn?

Summary:

In the diagram of circle a, m∠lmn = 90°