Question

12. PQRST is a regular pentagon. The bisector of angle P meets the side
RS at Z. Show that angle PZS = 90°.​

Answer 1

We know that sum of interior and exterior of a pentagon is 540° [(n-2)×180] and each angle = 108° .

therefore ..bisector angle P =54°

now in quadrilateral PQRZ

P+Q+R+Z=180°

therefore

54+108+108+PZR=360

270+PZR=360

PZR= 360-270=90

hence proved!.