Question

Afla măsurile unghiurilor triunghiului ABC in fiecare dintre cazurile de mai jos

Answer 1

$\bf a)\;Fie \; in\; C(O;r) : OC-raza$

$\bf BO;CO-raze \implies BC-diametru$

$\bf Stiim \; ca \; masura\; \angle \; opus \; diametrului \; in semicerc \; este\; de \; 90^{\circ}$

$\bf \implies \angle A=90^{\circ}$

$\bf \widehat{AC}=40^{\circ} \implies \angle B=\dfrac{\widehat{AC}}{2} =\dfrac{40^{\circ}}{2} =20^{\circ}$

$\bf \implies \angle C=180^{\circ}-\angle A-\angle B=180^{\circ}-90^{\circ}-20^{\circ}=70^{\circ}$

$\star$

$\bf b)\; \widehat{AB}=60^{\circ} \implies \angle C=\dfrac{\widehat{AB}}{2} =\dfrac{60^{\circ}}{2}=30^{\circ}$

$\bf \widehat{AC}=70^{\circ} \implies \angle B=\dfrac{\widehat{AC}}{2} =\dfrac{70^{\circ}}{2} =35^{\circ}$

$\bf \implies \angle A=180^{\circ}-\angle B-\angle C=180^{\circ}-35^{\circ}-30^{\circ}=115^{\circ}$

$\star$

$\bf c)\;BC-diametru \implies \angle A=90^{\circ}$

$\bf AB \equiv AC \implies \triangle ABC-isoscel$

$\bf \implies \angle B=\angle C=x^{\circ}$

$\bf Stim \; ca \; \angle A + \angle B + \angle C=180^{\circ}$

$\bf \implies 90^{\circ}+x+x=180 \implies 2x+90^{\circ}=180^{\circ}$

$\bf \implies 2x=180^{\circ}-90^{\circ}=90^{\circ}\:|:2$

$\bf \implies \angle B=\angle C=45^{\circ}$

$\star$

Bafta!

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