Question

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

Thank you for asking this question.  

Here is your answer:

Since BQ=BP and ∡QBP=90∘ (this is a right angle)

We obtain ∡BPT=45∘ (this would be the half of that angle)

And  

∡BTQ=∡BPT+∡PBT=45∘+40∘=85∘  

Please leave a comment below if you have any problems.

Answer 2

Since triangles BQC and APB are isosceles along with the same vertex angels, sides PB and QB are congruent.

This statement represents BQ = BP and angle QBP = 90degree. Making T the midpoint of PQ, you obtain angle BPT = 45degree and angle BTQ = angle BPT + angle PBT => 45degree + 40degree = 85degree.

Hence, the size of angle BTQ is 85degree.