Question

Does anyone know the answer to this? If so can u please help me.

Answer 1

`m\angle M = 90\degree\\</p><p>m\angle L = 24\degree`

Explanation:

LM is tangent to the circle at point M and NM is radius.

`\therefore NM\perp LM.. (radius \perp tangent) \\</p><p>\huge\orange {\boxed {m\angle M = 90\degree}} \\`

By interior angle sum postulate of a triangle, we have:

`m\angle L + m\angle M + m\angle N = 180\degree \\</p><p>m\angle L + 90\degree + 66\degree = 180\degree \\</p><p>m\angle L + 156\degree = 180\degree \\</p><p>m\angle L = 180\degree - 156\degree \\</p><p></p><p>\huge\red {\boxed {m\angle L = 24\degree}} \\`