Question

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 measure of the equal angles angles of the triangle?​

Answer 1

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°.

Answer 2

$\bf \underline{Given} :$

$\sf Exterior \: angle \: of \: a \: triangle = 140^{\circ}$

$\sf Interior \: opposite \: angles \: are \: equal \: to \: each \: other.$

$\bf \underline{To \: find} :$

$\sf Measurements \: of \: all \: angles \: of \: the \: triangle.$

$\bf \underline{\underline{Solution} }$

$\sf As \: we \: know \: that,$

$\sf \implies \underline{\sf Exterior \: angle = Sum \: of \: interior \: opposite \: angles}$

$\sf Let \: one \: of \: the \: interior \: angle \: be \: x.$

$\bf \underline{Then},$

$\sf \implies Exterior \: angle = x + x$

$\sf \implies 140^{\circ} = x + x$

$\sf \implies 140^{\circ} =2x$

$\sf \implies \dfrac{140}{2} = x$

$\sf \implies 70^{\circ} = x$

$\sf \underline{ Interior \: opposite \: angles \: are \: 70 ^{\circ} \: , \: 70 ^{\circ}}$

$\sf Now, we \: will \: find \: the \: 3^{rd} \: side \: of \: the \: triangle.$

$\sf We \: know \: that,$

${\sf \boxed{ \red{\sf Angle \: sum \: property \: of \: triangle= {180}^{\circ}}}}$

$\sf \implies So, 70^{\circ} + 70^{\circ} + y = 180^{\circ}$

$\sf \implies 140^{\circ} + y = 180^{\circ}$

$\sf \implies y = 180^{\circ} - 140^{\circ}$

$\sf \implies y = 40^{\circ}$

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