Question

VA ROG DIN TOT SUFLETUL REPEDE DAU COROANA

Answer 1

ABCD-paralelogram

⇒AB║DC; BC║AD⇒AB=DC; BC=AD (1)

⇒∡A=∡C; ∡B=∡D (∡opuse) (2)

⇒∡ alaturate unei laturi sunt suplementare (=180°) (3)

⇒m(∡A)+m(∡B)+m(∡C)+m(∡D)=360° (4)

AB=BC+3cm

P=50cm

din (1)⇒AB=DC=BC+3cm

P=AB+BC+CD+AD

P=BC+3cm+BC+BC+3cm+BC

P=4BC+6cm

4BC+6cm=50cm

4BC=50cm-6cm

4BC=44cm

⇒BC=44cm/4=11cm

⇒AB=DC=BC+3cm=11cm+3cm=14cm

⇒BC=AD=11cm

din (2) si (3) ⇒m(∡B)=m(∡D)=130°

                    ⇒m(∡A)=m(∡C)=180°-130°=50°