Answer:
\(m\angle ABO\)=\(35^{\circ}\)
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 .
\(m\angle AOB=55^{\circ}\)
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,\(m\angle OAB=90^{\circ}\)
We know that sum of angles of a triangle is \(180^{\circ}\).
By sum of angle of triangle property
Therefore,in triangle OAB
\(m\angle\)OAB+ \(m\angle\)ABO+ \(m\angle\)AOB=\(180^{\circ}\)
By angle sum of triangle property
90+55+\(m\angle ABO=180\)
\(145+m\angle ABO=180\)
\(m\angle ABO=180-145=35^{\circ}\)
Hence, the angle ABO=\(35^{\circ}\).
