Question

8. The exterior angles of a triangle are 3y 4 and 5y () Find the value of y. G) Find the smallest interior angle of the triangle​

Answer 1

$1) \: 3y = 180 - a$

$Exterior \: \angle = {180}^{o} - Interior \: \angle$

$a \: = 180 - 3y$

$2) \: 4y = 180 - b$

$b \: = 180 - 4y$

$3) \:5 y = 180 - c$

$c = 180 - 5y$

$in \: \triangle \: sum \: of \: angles \: = 180$

$a + b + c \: = 180$

$180 - 3y + 180 - 4y + 180 - 4y = 180$

$180 + 180 + 180 - 3y - 4y - 4y =180$

$540 - 11y = 180$

$- 11y = 180 - 540$

$- 11y = - 360$

$y = - \cancel\frac { - 360}{ - 11}$

$y = 32.78$

$y \: is \: the \: smallest \: interior \: \angle \: of \: the \: triangle.$