Question

AB and BC are tangents to P. what is the value of x? this is really so confusing

Answer 1

1. Angle PAB is 90 degrees, as it is formed from the tanget to the circle at A, and the radius drawn to A. 

2. AB=BC, because tangents drawn to a circle from the same point are equal.

3. PB is Common, so by the side-side-side congruence postulate, triangles ABP and CBP are congruent. 

4. So measure of m(BPA)=x/2 and m(ABP)=73/2.

5. $\frac{x}{2}+90+ \frac{73}{2}=180$

$\frac{x+73}{2}=90$

$x+73=180$, x= 107 degrees.