ray pb bisects < rpt so that < rpb = x+2 and < tpb = 2x-6. What is < rpt =

since PB is the bisector, the other two angles are equal.

x+2 = 2x-6

solve for x, and then you can find your angle.

To find the measure of angle <RPT, we need to use the properties of angles formed by a bisector.

The angle <RPB and <TPB are formed by the bisector, so according to the Angle Bisector Theorem, the ratio of the measures of these angles is equal to the ratio of the lengths of the sides that the bisector intersects.

In this case, the ratio is:

<RPB / <TPB = RP / TP

Given that <RPB = x + 2 and <TPB = 2x - 6, we can set up the equation:

(x + 2) / (2x - 6) = RP / TP

To solve for x, we can cross-multiply:

(RP)(x + 2) = (TP)(2x - 6)

Now, we can solve for RP/TP in terms of x.