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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
avatar+7155 
+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
avatar+7002 
+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

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