In a square ABCD, point P is chosen inside ABCD and point Q outside ABCD such that APB and BQC are congruent isosceles triangles with angle APB = angle BQC = 80 degrees. T is a point where BC and PQ meet. Find the size of angle BTQ

Answer 1

since triangles APB and BQC are isosceles with the same vertex angles, sides PB and QB are congruent.
That means triangle BPQ is isosceles, making T the midpoint of PQ.
Angles BTP and BTQ are right angles.