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Marysya12 [62]
3 years ago
5

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

Mathematics
2 answers:
777dan777 [17]3 years ago
4 0

Answer:

<h3>m\angle ABO=35^{\circ}</h3>

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\angleOAB+ m\angleABO+ m\angleAOB=180^{\circ}

By angle sum of triangle property

90+55+m\angle ABO=180

145+m\angle ABO=180

<h3>m\angle ABO=180-145=35^{\circ}</h3><h3>Hence, the angle ABO=35^{\circ}.</h3>

AlladinOne [14]3 years ago
3 0
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
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