AC is tangent to the circle with center at B. The measure of ∠ACB is 71°.

What is the measure of ∠ABC?

Guest Mar 21, 2017

#1**+2 **

m∠BAC = 90º

m∠ACB = 71º

m∠ABC + m∠ACB + m∠BAC = 180º

m∠ABC + 71º + 90º = 180º

Now just solve for m∠ABC.

m∠ABC = 180º - 71º - 90º

m∠ABC = 19º

hectictar
Mar 21, 2017

#2**+1 **

If you construct a line from the center to any point on the circumference and construct a tangent on that line, the lines always are perpendicular.

Therefore ∠BAC = 90 degrees.

Therefore use the Angle Sum of Triangles:

90 + 71 + ∠ABC = 180

∠ABC = 19 degrees :)

~The smartest cookie in the world

MaxWong
Mar 22, 2017