Question

Fie ABCD romb si (CE bisectoarea unghiului ACB, E∈(AB). Daca m(∡BEC)= 48°, aflati m(∡BAD) si m(∡ABC).

Answer 1

notam m(∡ABC)=x
2x+2×m(∡BCD)=360°
x+m(∡BCD)=180°
m(∡BCD)=180°-x
m(∡BAC)=m(∡BCA)=m(∡BCD)/2
m(∡BCE)=m(∡BCD)/4=(180°-x)/4
in triunghiul BEC   suma unghiurilor esate :
 x+48°+(180°-x)/4=180°
4x+192°+180°-x=720°
3x=348°
x=116°
m(∡ABC)=m(∡ADC)=116°
m(∡BAD)=m(∡BCD)=180°-116°=64°