AC←→ is tangent to the circle with center at B. The measure of ∠ACB is 58°. What is the measure of ∠ABC ?

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3 Answers
Mar 17, 2018

ABC=32

Explanation:

BAC=90( angle between tangent and radius)

angle sum of ABC=180

ABC=180(90+58)=32

Mar 17, 2018

58°

Explanation:

The answer is given in the question

Mar 17, 2018

ABC=32

Explanation:

Let's start out by laying out what we know:

1) AC is tangent to the circle

2) Since AC is tangent to the circle, we know that it forms a right angle with the radius AB. So A=right angle=90

3) ACB=58 (this angle is the same as C which is what I'm going to call it.)

Do you see that little triangle that's inside the circle? Well we know that the angles of a triangle add up to 180, we can make this into an equation:

A+ABC+C=180

Let's substitute into this equation since we know some of the angles:

A+ABC+C=180
90+ABC+58=180
148+ABC=180
ABC=32