Point p is inside triangle abc and equidistant from all three sides. if the measure of angle abc=60°, what is the measure of angle pbc?

∠PBC = 30°

Step-by-step explanation:

Given that <ABC = 60° and P is equidistance from AB, AC, BC  

If P is equidistance from all the side then triangle ABC is equilateral    

<ABC = <ACB = <CAB =60 and P is the center of the triangle (characteristics of an equilateral triangle)

If a perpendicular line is drawn from any of the angle through P to any of the opposite side it will divide the side into equal length  

For instance AB = AC = BC = 2CM  

If we draw a perpendicular line from <ABC through P to AC at point D  

Then we will have a right angle triangle BCD : < BDC =90, BC = 2CM, CD =1CM  

We can use sine rule to determine the angle  

Sine BDC    =    sine CBD

BC                  CD

Sine 90   = sine CBD  

2                1

1      =     sine CBD

2                     1      

sin CBD = 0.5

<CBD  = 30°  

<CBD = <PBC = 30°

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