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

angleABC=32^@

Explanation:

angleBAC=90^@to(" angle between tangent and radius")

"angle sum of "triangleABC=180^@

rArrangleABC=180^@-(90+58)^@=32^@

Mar 17, 2018

58°

Explanation:

The answer is given in the question

Mar 17, 2018

angleABC = 32^@

Explanation:

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

1) stackrel_"AC" is tangent to the circle

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

3) /_ACB=58^@ (this angle is the same as angleC 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:

angleA + angleABC + angleC = 180^@
90^@ + angleABC + 58^@ = 180^@
148^@+ angleABC = 180^@
angleABC = 32^@