Question

AB ← → is tangent to circle O at point A. If m∠AOB = 55°, what is m∠ABO ?

Answer 1

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=$35^{\circ}$.

Answer 2

A tangent forms a right angle with the centre of circle at the point it touches the circumference. i.e. OAB = 90 degrees
If AOB = 55 degrees, then ABO = 90 - 55 = 35 degrees