Question

Masurile unghiurilor A,B si C ale triunghiului ABC sunt direct proportionale cu numerele 4, 5, 3. Perpendiculara in C pe BC intersecteaza paralela prin A la BC in pctul D. Calculati masurile unghiurilor patrulaterului ABCD.

Answer 1

$\dfrac{m(A)}{4}=\dfrac{m(B)}{5}=\dfrac{m(C)}{3}=\dfrac{180}{12}=15^{\circ}$

$\dfrac{m(A)}{4}=15\Rightarrow m(A)=60^{\circ}$

$\dfrac{m(B)}{5}=15\Rightarrow m(B)=75^{\circ}$

$\dfrac{m(C)}{3}=15\Rightarrow m(A)=45^{\circ}$

$m(DBC)=90^{\circ}\Rightarrow m(D)=90^{\circ};\ \ (AD||BC \ si\ DC\bot BC\Rightarrow DC\bot AD)$

$m(DAB)=360^{\circ}-\left(m(B)+m(BCD)+m(D)\right)=360-255=105^{\circ}$