Respuesta :

Answer:

see explanation

Step-by-step explanation:

Since AB = BC the the triangle is isosceles and thus

∠ A = ∠ C = 8x

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

44x + 8x + 8x = 180, that is

60x = 180 ( divide both sides by 60 )

x = 3

Thus

∠ A = ∠ C = 8x = 8(3) = 24°

∠ B = 44x = 44(3) = 132°

Step-by-step explanation:

[tex] In\: \triangle ABC\\\\

BA = BC... (Given) \\\\

\therefore \angle BAC = \angle BCA \\(Angles \:opposite\: to \:equal\:\\sides\:are\: equal) \\\\

\because m\angle BCA= 8x... (Given) \\\\

\therefore \angle BAC = 8x\\\\

In\: \triangle ABC\\\\

m\angle ABC + m\angle BAC + m\angle BCA \\= 180\degree \\\\

\therefore \: 44x + 8x + 8x = 180\degree \\\\

\therefore \: 60x= 180\degree \\\\

\therefore \: x= \frac{180\degree}{60} \\\\

\therefore \: x= 3\degree\\\\

\therefore \: m\angle B =44x = 44\times 3\degree\\\\

\therefore \: m\angle B =132\degree\\\\

m\angle A= m\angle C=8x =8 \times 3\degree\\\\

\therefore \: m\angle A= m\angle C= =24\degree[/tex]