Question

Aflati masura celui de-al treilea unghi al unui triunghi si masura unghiului exterior lui, daca celelalte doua unghiuri au masurile de: a). 30°; 40° , b). 25°;85°, c). 30° 20' , 45°; 30', d). 45° 35' 42''; 56° 42' 35" .

Answer 1

Unghiurile A, B si C.

Intr-un triunghi avem:

a) m(∡A)+m(∡B)+m(∡C)=180°⇔
⇔30°+40°+m(∡C)=180°⇔
⇔70°+m(∡C)=180°⇔
⇔m(∡C)=180°-70°⇔
⇔m(∡C)=110°
Cel de-al 3-lea unghi are masura de 110°.

b)m(∡A)+m(∡B)+m(∡C)=180°⇔
⇔25°+85°+m(∡C)=180°⇔
⇔110°+m(∡C)=180°⇔
⇔m(∡C)=180°-110°⇔
⇔m(∡C)=70°
Cel de-al treilea unghi are masura de 70°.

c)m(∡A)+m(∡B)+m(∡C)=180°⇔
⇔45°30'+30°20'+m(∡C)=180°⇔
⇔75°50'+m(∡C)=180°⇔
⇔m(∡C)=180°-75°50'⇔
⇔m(C)=104°10'
Cel de-al treilea unghi are masura de 104°10'.

d)m(∡A)+m(∡B)+m(∡C)=180°⇔
⇔45°35'42''+56°42'35''+m(∡C)=180°⇔
⇔102°18'17''+m(∡C)=180°⇔
⇔m(∡C)=180°-102°18'17''⇔
⇔m(∡C)=77°41'43''
Cel de-al 3-lea unghi are masura de 77°41'43''.