Question

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

What is the measure of ∠ABC?



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Answer 1

I'm pretty sure the answer is '19' but if i'm wrong please don't kill me.

Answer 2

In the given circle, radius is perpendicular to tangent.

So that means AB⊥AC

so ∠BAC =90°......(1)

Also we are given ∠ACB =71°................(2)

Now we will use angle sum property of a triangle here.

It states that sum of three angles of a triangle is 180° .

Applying this property here,

∠A +∠B +∠C =180°.............(3)

Plugging values from equation (1) and (2) in (3)

∠A +∠B +∠C =180°

90 +∠B +71 =180°

161 + ∠B = 180°

∠B = 19°

Answer: Angle ABC is 19 degrees.