if an exterior angle of a triangle is 140°and it’s opposite interior angles are equal to each other, which of the following is the

2 thoughts on “if an exterior angle of a triangle is 140°and it’s opposite interior angles are equal to each other, which of the following is the”

1. [tex] \bf \underline{Given} :[/tex]

   [tex] \sf Exterior \: angle \: of \: a \: triangle = 140^{\circ}[/tex]

   [tex] \sf Interior \: opposite \: angles \: are \: equal \: to \: each \: other.[/tex]

   [tex] \bf \underline{To \: find} :[/tex]

   [tex] \sf Measurements \: of \: all \: angles \: of \: the \: triangle.[/tex]

   [tex] \bf \underline{\underline{Solution} }[/tex]

   [tex] \sf As \: we \: know \: that, [/tex]

   [tex]\sf \implies \underline{\sf Exterior \: angle = Sum \: of \: interior \: opposite \: angles}[/tex]

   [tex] \sf Let \: one \: of \: the \: interior \: angle \: be \: x. [/tex]

   [tex] \bf \underline{Then}, [/tex]

   [tex]\sf \implies Exterior \: angle = x + x [/tex]

   [tex]\sf \implies 140^{\circ} = x + x [/tex]

   [tex]\sf \implies 140^{\circ} =2x [/tex]

   [tex]\sf \implies \dfrac{140}{2} = x [/tex]

   [tex]\sf \implies 70^{\circ} = x [/tex]

   [tex] \sf \underline{ Interior \: opposite \: angles \: are \: 70 ^{\circ} \: , \: 70 ^{\circ}}[/tex]

   [tex] \sf Now, we \: will \: find \: the \: 3^{rd} \: side \: of \: the \: triangle.[/tex]

   [tex] \sf We \: know \: that, [/tex]

   [tex]{\sf \boxed{ \red{\sf Angle \: sum \: property \: of \: triangle= {180}^{\circ}}}}[/tex]

   [tex]\sf \implies So, 70^{\circ} + 70^{\circ} + y = 180^{\circ}[/tex]

   [tex]\sf \implies 140^{\circ} + y = 180^{\circ}[/tex]

   [tex]\sf \implies y = 180^{\circ} – 140^{\circ}[/tex]

   [tex]\sf \implies y = 40^{\circ}[/tex]

   [tex]{\underline{\boxed{\sf \pink{ So, \: all \: angles \: of \: triangle \: are \: {70}^{\circ}, \: {70}^{\circ} \: and\:{40}^{\circ}.}}}}[/tex]

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2. Answer:

   = 70°

   Step-by-step explanation:

   Interior opposite angle are equal. Let one of the interior opposite angle be x. Then x + x = 140°. Interior opposite angle = 70°, 70°.

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