Question

In the given figure, PN and UL are respectively the bisectors of angle P and angle U of a quadrilateral JUMP meet MU and JP produced in N and L. Prove that:
angle JPM + angle JUM =2(angle N + angle L)

Answer 1

In ∆NPM
angle N+angle NPM+angleM = 180°
In ∆JUL
angle J+angle JUL+angle L = 180°
By adding

angle N+angle NPM+angleM+angle J+angle JUL+angle L = 360°

But, 360° = angle J+angle M+2 angle JUL+2 angle NPM

angle N+angle NPM+angleM+angle J+angle JUL+angle L = angle J+angle M+2 angle JUL+2 angle NPM


From this we get
angle JPM + angle JUM =2(angle N + angle L