Answer:
[tex]m\angle ABO[/tex]=[tex]35^{\circ}[/tex]
Step-by-step explanation:
Given AB is a tangent to the circle O and touch the circle at point A.
We know that tangent is a line which touches the circle only at one point .
[tex]m\angle AOB=55^{\circ}[/tex]
We know that the radius of circle is perpendicular to the tangent.
In the figure OA is radius of given circle
AB is a tangent line
Radius OA is perpendicular to the tangent AB.
Therefore,[tex]m\angle OAB=90^{\circ}[/tex]
We know that sum of angles of a triangle is [tex]180^{\circ}[/tex].
By sum of angle of triangle property
Therefore,in triangle OAB
[tex]m\angle[/tex]OAB+ [tex]m\angle[/tex]ABO+ [tex]m\angle[/tex]AOB=[tex]180^{\circ}[/tex]
By angle sum of triangle property
90+55+[tex]m\angle ABO=180[/tex]
[tex]145+m\angle ABO=180[/tex]
[tex]m\angle ABO=180-145=35^{\circ}[/tex]
Hence, the angle ABO=[tex]35^{\circ}[/tex].
