+0  
 
+1
245
2
avatar

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
Sort: 

2+0 Answers

 #1
avatar+5552 
+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+6900 
+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

17 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details