Question

AB ← → is tangent to circle O at point A. If m∠AOB = 72degrees what is m∠ABO ?

Answer 1

Answer:

$m\angle ABO=18^o$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If AB is tangent to circle O at point A

then

AB is perpendicular to AO (radius) and Triangle ABO is a right triangle

so

$m\angle ABO+m\angle AOB=90^o$ ----> by complementary angles in a right triangle

substitute the given value

$m\angle ABO+72^o=90^o$

$m\angle ABO=90^o-72^o=18^o$