Geometry help - kids homework

WOW!! That is confusing, I never really understood it at school. I am replying to this so I can find the discussion again easily when there are more responses hopefully with an answer and an explanation of how to do it because I cannot work it out for the life of me and would love to know how to nwork thi ngs like that out!

Hi! If I remember my geometry correctly an isosceles triangle means a triangle with 2 equal sides. Since one of the angles is equal to 60 degrees, it simply means that the angles ACB and CBA are also 60 degrees because the sum of interior angles of a triangle should always be equal to 180 degrees right? Therefore you also have an equilateral triangle which means that all your angles and sides have the same values. So if a line bisects angle ABC, you'll have a 60-30-90 degree angles.

Given ABC is an isosceles triangle with AB=AC then angle b= angle c by base angles theorem(If 2 opposite sides of a triangle are= then the angles opposite them are=.)
A triangle have 180 degrees in total so it's 180 - 60= 120 and divide by 2 (the 2 other angles are equal to each other) making the other angles having the measure of 60.
The line PB bisects the angle ABC(A bisector cuts an angle into 2 congruent/equal angles) mean that angle ABP= angle PBC. So 60 divided by 2= 30 which is the measure of angle ABP and PBC.
...Problem is that we don't know the measure of angle PAC or that if AP and BC are parallel

Hello friend,
Its a bit confusing.
Its given that ABC is a isosceles triangle,as the angle BAC=60 degree,its a equilateral triangle too.ie,AB=BC=CA.
The angle Bisector of a equilateral triangle will bisect the opposite side and will be perpendicular to the opposite side.
So AC=CD, and AC perpendicular to BP.

For further steps,
AP should be parallel to BC,in the Picture its not seems so.
If AP parallel to BC,we can say ABCP is a parallelogram.
right?( As diagonals are perpendicular bisectors and AD=CD)
So we get,
angle CBP and angle BPA (ie,x) are equal.
ie, x=30 degrees.
Am i right friend?