Question

one of the exterior angle of a triangle ABC measures 150 degree. if one of the interior opposite angle is 75 degree.find the other interior opposite angle.what type of triangle is this​

Answer 1

It is given that, one of the exterior angle of a ∆ ABC measures 150°.

And, one of the interior opposite angle is 75°.

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We have to find, The other interior opposite angle.

And the type of triangle.

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☯ Let another interior angle of ∆ ABC be x.

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Therefore,

$:\implies\sf x + 75^\circ = 150^\circ$

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$:\implies\sf x = 150^\circ - 75^\circ$

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$:\implies{\underline{\boxed{\bf{x = 75^\circ}}}}\;\bigstar$

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☯ Let assume the third angle of ∆ ABC be y.

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Therefore,

$:\implies\sf 75^\circ + 75^\circ + y = 180^\circ\;\;\;\;\;\bigg\lgroup\bf Angle\;sum\;property \bigg\rgroup$

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$:\implies\sf 150^\circ + y = 180^\circ$

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$:\implies\sf y = 180^\circ - 150^\circ$

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$:\implies{\underline{\boxed{\bf{y = 30^\circ}}}}\;\bigstar$

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Therefore, If two angle of ∆ are equal then, the opposite sides of equal angles are also equal.

So, We can say that the given ∆ ABC is Isosceles.

Hence, The another interior opposite angle is 75° and the given triangle is Isosceles.