Question

a quadrilateral PQRS, PQ is its longest side and RS is its shortest side. Prove that angle R is greater than angle P and angle S is greater than angle Q

Answer 1

construction : join PR
in triangle PRS, RS is shortest side.
so, angle SPR is shortest angle
angle opposite to shortest side is shortest
angle SRP > angle SPR. ------------------1

in triangle PQR, PQ is longest side
so, angle PRQ is greatest angle
angle opposite to longest side of greatest
angle PRQ > angle QPR. -------------------2

1+2

angle SRP + angle PRQ > angle SPR + angle QPR
angle R > angle P

hence proved

hope you understand my answer xD

Answer 2

Answer:

this is the answer and explanation