Question

One of the exterior angles of a triangle is 30 degree and the interior opposite angles are in the ratio 2 ratio 3.Find the angles of the triangle

Answer 1

The angles will be 52°,78° and 50 °

Answer 2

Let the opposite interior angles of the triangle be 2x and 3x

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• Sum of to opposite interior angles equal to an exterior angle in a triangle

$\\ { : \implies} \sf \: 30 \degree = 2x + 3x \\ \\ \\ { : \implies} \sf \: 30 \degree = 5x \\ \\ \\ { : \implies} \sf \:x = \cancel\frac{30}{5} \\ \\ \\ { : \implies} { \underline{ \boxed{ \sf \: x \degree =6 \degree \: }}}$

$\\ \\ \sf \: the \: angle \: 2x = 6(2) = \pink{12\degree} \\ \\ \sf \: the \: angle \: 3x = 6(3) = \pink{18\degree}$

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• Sum of interior angles in a triangle is 180°

$\sf \longrightarrow\angle \: 12 \degree + \angle \: 18 + \angle \: c \degree = 180\degree \\ \\ \\ \sf \longrightarrow\angle \: 30 \degree+ \angle \: c = 180\degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow\sf\angle \: c\degree = 180 - 30\degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow\sf {\underline{\boxed{ \pink{ \sf\angle c\degree = 150\degree }}}}\bigstar \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hope this helps:)